92 results on '"Gemai Chen"'
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2. Projection sparse principal component analysis: An efficient least squares method.
- Author
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Giovanni Maria Merola and Gemai Chen
- Published
- 2019
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3. Case deletion diagnostics for GMM estimation.
- Author
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Lei Shi 0004, Jun Lu, Jianhua Zhao, and Gemai Chen
- Published
- 2016
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4. Estimation and inference for varying-coefficient regression models with error-prone covariates.
- Author
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Yongqing Xu, Xiaoli Li 0003, and Gemai Chen
- Published
- 2014
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5. A Note on the Likelihood Ratio Test for Equality of k Normal Populations.
- Author
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Lingyun Zhang, Dong Q. Wang, Min Chen, and Gemai Chen
- Published
- 2012
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- View/download PDF
6. Deletion, replacement and mean-shift for diagnostics in linear mixed models.
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Lei Shi 0004 and Gemai Chen
- Published
- 2012
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- View/download PDF
7. Asymptotic Normality for EMS Option Price Estimator with Continuous or Discontinuous Payoff Functions.
- Author
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Zhushun Yuan and Gemai Chen
- Published
- 2009
- Full Text
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8. On t and EWMA t charts for monitoring changes in the process mean.
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Lingyun Zhang, Gemai Chen, and Philippe Castagliola
- Published
- 2009
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- View/download PDF
9. Projection sparse principal component analysis: An efficient least squares method
- Author
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Gemai Chen and Giovanni Maria Merola
- Subjects
Statistics and Probability ,Numerical Analysis ,Dimensionality reduction ,020206 networking & telecommunications ,Feature selection ,02 engineering and technology ,Variance (accounting) ,01 natural sciences ,Least squares ,010104 statistics & probability ,Cardinality ,Power iteration ,Principal component analysis ,0202 electrical engineering, electronic engineering, information engineering ,0101 mathematics ,Statistics, Probability and Uncertainty ,Projection (set theory) ,Algorithm ,Mathematics - Abstract
We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a given proportion of variance. The computation of these solutions is very efficient. The proposed method compares well with the optimal least squares sparse components. We show that other SPCA methods fail to identify the best sparse approximations of the principal components and explain less variance than our solutions. We illustrate and compare our method with others with extensive simulations and with the analysis of the computational results for nine datasets of increasing dimensions up to 16,000 variables.
- Published
- 2019
10. Graphing Kendall's tau.
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Matthew K. Davis and Gemai Chen
- Published
- 2007
- Full Text
- View/download PDF
11. Some specific density functions of aggregated discounted claims with dependent risks
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Gemai Chen and Zhehao Zhang
- Subjects
Arrival process ,Applied Mathematics ,Dependent risks ,Poisson process ,Mixed Poisson process ,Specific density ,Exponential function ,Cox process ,symbols.namesake ,Mixing ,Generalized Pareto distribution ,QA1-939 ,symbols ,Applied mathematics ,Beta (velocity) ,Special functions and transforms ,Discounted claims ,Mathematics ,Mixing (physics) - Abstract
This paper obtains some specific density functions for aggregated discounted claims where the claim amounts are dependent, or the inter-claim times are dependent, or the claim amounts and the claim arrival process are both dependent. The dependence is structured through mixing, and the claim arrival process studied is either an ordinary Poisson process or a mixed Poisson process. Closed form densities are obtained for gamma, generalized exponential, generalized Pareto and beta mixing, and an important use of them is illustrated.
- Published
- 2021
12. Percentage points and power of a K-S type test for linearity in autoregressive time series
- Author
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Gemai, Chen, Min, Chen, and Guofu, Wu
- Published
- 2001
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13. Case deletion diagnostics for GMM estimation
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Gemai Chen, Jianhua Zhao, Jun Lu, and Lei Shi
- Subjects
Statistics and Probability ,Applied Mathematics ,05 social sciences ,Instrumental variable ,Estimator ,Residual ,01 natural sciences ,010104 statistics & probability ,Computational Mathematics ,Econometric model ,Nonlinear system ,Computational Theory and Mathematics ,0502 economics and business ,Outlier ,Econometrics ,Applied mathematics ,Leverage (statistics) ,0101 mathematics ,050205 econometrics ,Mathematics ,Panel data - Abstract
Generalized method of moment (GMM) is an important estimation method for econometric models. However, it is highly sensitive to the outliers and influential observations. This paper studies the detection of influential observations using GMM estimation and establishes some useful diagnostic tools, such as residual and leverage measures. The case deletion technique is employed to derive diagnostic measures. Under linear moment conditions, an exact deletion formula is derived, and under nonlinear moment condition an approximate formula is suggested. The results are applied to efficient instrumental variable estimation and dynamic panel data models. In addition, generalized residuals and leverage measure for GMM estimator are defined and discussed. Two real data sets are used for illustration and a simulation study is conducted to confirm the usefulness of the proposed methodology.
- Published
- 2016
14. Statistical inference for multivariate partially linear regression models
- Author
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Jinhong You, Yong Zhou, and Gemai Chen
- Subjects
Statistics and Probability ,Multivariate statistics ,Statistics ,Linear regression ,Econometrics ,Nonparametric statistics ,Statistical inference ,Asymptotic distribution ,Estimator ,Statistics, Probability and Uncertainty ,Regression ,Parametric statistics ,Mathematics - Abstract
In this paper we study a class of multivariate partially linear regression models. Various estimators for the parametric component and the nonparametric component are constructed and their asymptotic normality established. In particular, we propose an estimator of the contemporaneous correlation among the multiple responses and develop a test for detecting the existence of such contemporaneous correlation without using any nonparametric estimation. The performance of the proposed estimators and test is evaluated through some simulation studies and an analysis of a real data set is used to illustrate the developed methodology. The Canadian Journal of Statistics 41: 1–22; 2013 © 2013 Statistical Society of Canada Dans cet article, nous etudions une classe de modeles de regression multivariee partiellement lineaires. Nous developpons plusieurs estimateurs des composantes parametrique et non parametrique et etablissons leur normalite asymptotique. Nous proposons notamment un estimateur de la correlation contemporaine parmi les reponses multiples et nous construisons un test pour detecter l'existence d'une telle correlation sans utiliser aucune estimation non parametrique. La performance des estimateurs et du test proposes est evaluee par le biais d'etudes de simulation et la methodologie elaboree est illustree par l'analyse d'un ensemble de donnees reelles. La revue canadienne de statistique 41: 1–22; 2013 © 2013 Societe statistique du Canada
- Published
- 2013
15. The Exact Likelihood Ratio Test for Equality of Two Normal Populations
- Author
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Gemai Chen, Lingyun Zhang, and Xinzhong Xu
- Subjects
Statistics and Probability ,Score test ,General Mathematics ,Pearson's chi-squared test ,Likelihood principle ,symbols.namesake ,Exact test ,Multinomial test ,Likelihood-ratio test ,Statistics ,symbols ,Z-test ,F-test of equality of variances ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
Testing the equality of two independent normal populations is a perfect case of the two-sample problem, yet it is not treated in the main text of any textbook or handbook. In this article, we derive the exact distribution of the likelihood ratio test and implement this test with an R function. This article has supplementary materials online.
- Published
- 2012
16. A Note on the Likelihood Ratio Test for Equality ofkNormal Populations
- Author
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Dong Q. Wang, Lingyun Zhang, Min Chen, and Gemai Chen
- Subjects
Statistics and Probability ,Modeling and Simulation ,Likelihood-ratio test ,Statistics ,Null distribution ,Variance (accounting) ,Beta (finance) ,Mathematics - Abstract
The authors derive the analytic expressions for the mean and variance of the log-likelihood ratio for testing equality of k (k ≥ 2) normal populations, and suggest a chi-square approximation and a gamma approximation to the exact null distribution. Numerical comparisons show that the two approximations and the original beta approximation of Neyman and Pearson (1931) are all accurate, and the gamma approximation is the most accurate.
- Published
- 2012
17. Deletion, replacement and mean-shift for diagnostics in linear mixed models
- Author
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Lei Shi and Gemai Chen
- Subjects
Statistics and Probability ,General linear model ,Restricted maximum likelihood ,Covariance matrix ,Applied Mathematics ,Generalized linear mixed model ,Computational Mathematics ,Computational Theory and Mathematics ,Linear regression ,Outlier ,Statistics ,Applied mathematics ,Case deletion ,Mean-shift ,Mathematics - Abstract
Deletion, replacement and mean-shift model are three approaches frequently used to detect influential observations and outliers. For general linear model with known covariance matrix, it is known that these three approaches lead to the same update formulae for the estimates of the regression coefficients. However if the covariance matrix is indexed by some unknown parameters which also need to be estimated, the situation is unclear. In this paper, we show under a common subclass of linear mixed models that the three approaches are no longer equivalent. For maximum likelihood estimation, replacement is equivalent to mean-shift model but both are not equivalent to case deletion. For restricted maximum likelihood estimation, mean-shift model is equivalent to case deletion but both are not equivalent to replacement. We also demonstrate with real data that misuse of replacement and mean-shift model in place of case deletion can lead to incorrect results.
- Published
- 2012
18. A Note on Bartlett'sMTest for Homogeneity of Variances
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Wenjiang Jiang, Lingyun Zhang, and Gemai Chen
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Statistics and Probability ,Analysis of covariance ,Statistics::Machine Learning ,Statistics::Theory ,Homogeneity (statistics) ,Statistics ,Statistics::Methodology ,F-test of equality of variances ,Bartlett's test ,Mathematics - Abstract
After pointing out a drawback in Bartlett's chi-square approximation, we suggest a simple modification and a Gamma approximation to improve Bartlett's M test for homogeneity of variances.
- Published
- 2010
19. Weighted profile least squares estimation for a panel data varying-coefficient partially linear model
- Author
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Qinfeng Xu, Gemai Chen, Bin Zhou, and Jinhong You
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Polynomial ,Goodness of fit ,Applied Mathematics ,General Mathematics ,Statistics ,Nonparametric statistics ,Linear model ,Estimator ,Generalized least squares ,Nonparametric regression ,Parametric statistics ,Mathematics - Abstract
This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model (due to Baltagi 1995) to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator (WPLSE) and a weighted local polynomial estimator (WLPE) for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator (PLSE), and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator (LPE). The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll (2000) and Lin and Carroll (2000), ignoring the correlation structure entirely and “pretending” that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups. Some simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.
- Published
- 2010
20. Strong consistency of the empirical martingale simulation option price estimator
- Author
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Gemai Chen and Zhu-shun Yuan
- Subjects
Computer Science::Computer Science and Game Theory ,Valuation of options ,Applied Mathematics ,Monte Carlo methods for option pricing ,Computer Science::Multimedia ,Econometrics ,Strong consistency ,Estimator ,Black–Scholes model ,Martingale (probability theory) ,Lipschitz continuity ,Contract price ,Mathematics - Abstract
A simulation technique known as empirical martingale simulation (EMS) was proposed to improve simulation accuracy. By an adjustment to the standard Monte Carlo simulation, EMS ensures that the simulated price satisfies the rational option pricing bounds and that the estimated derivative contract price is strongly consistent with payoffs that satisfy Lipschitz condition. However, for some currently used contracts such as self-quanto options and asymmetric or symmetric power options, it is open whether the above asymptotic result holds. In this paper, we prove that the strong consistency of the EMS option price estimator holds for a wider class of univariate payoffs than those restricted by Lipschitz condition. Numerical experiments demonstrate that EMS can also substantially increase simulation accuracy in the extended setting.
- Published
- 2009
21. Asymptotic Normality for EMS Option Price Estimator with Continuous or Discontinuous Payoff Functions
- Author
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Gemai Chen and Zhu-shun Yuan
- Subjects
Computer Science::Computer Science and Game Theory ,empirical martingale simulation, Monte Carlo, Black-Scholes, GARCH, options, regression analysis, asymptotic normality, coverage rate ,Strategy and Management ,Autoregressive conditional heteroskedasticity ,Stochastic game ,Monte Carlo method ,Asymptotic distribution ,Estimator ,Black–Scholes model ,Management Science and Operations Research ,Piecewise linear function ,Martingale (probability theory) ,Mathematical economics ,Mathematics - Abstract
Empirical martingale simulation (EMS) was proposed by Duan and Simonato (Duan, J.-C., J.-G. Simonato. 1998. Empirical martingale simulation for asset prices. Management Sci. 44(9) 1218–1233) as an adjustment to the standard Monte Carlo simulation to reduce simulation errors. The EMS price estimator of derivative contracts was shown to be asymptotically normally distributed in Duan et al. (Duan, J.-C., G. Gauthier, J.-G. Simonato. 2001. Asymptotic distribution of the EMS option price estimator. Management Sci. 47(8) 1122–1132) when the payoffs are piecewise linear and continuous. In this paper, we extend the asymptotic normality result to more general continuous payoffs, and for discontinuous payoffs we make a conjecture.
- Published
- 2009
- Full Text
- View/download PDF
22. Case deletion diagnostics in multilevel models
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Gemai Chen and Lei Shi
- Subjects
Statistics and Probability ,Multilevel models ,030506 rehabilitation ,Numerical Analysis ,Multivariate analysis ,Estimation theory ,Multilevel model ,Cook’s distance ,Random parameters ,Case deletion ,01 natural sciences ,010104 statistics & probability ,03 medical and health sciences ,primary ,Calculus ,Applied mathematics ,Influential observations ,0101 mathematics ,Statistics, Probability and Uncertainty ,secondary ,0305 other medical science ,Cook's distance ,Mathematics - Abstract
This paper studies case deletion diagnostics for multilevel models. Using subset deletion, diagnostic measures for identifying influential units at any level are developed for both fixed and random parameters. Two approximate update formulae are derived. The first formula uses one-step approximation, while the second formula also includes the impact of estimating the random parameter. Two examples are used to illustrate the methodology developed.
- Published
- 2008
23. Local influence in multilevel models
- Author
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Gemai Chen and Lei Shi
- Subjects
Statistics and Probability ,Linear regression ,Multilevel model ,Statistics ,Applied mathematics ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
The authors study the local influence of observations in multilevel regression models. To this end, they perturb simultaneously the variances, responses and design matrix. To measure the local change caused by these perturbations, they use generalized Cook statistics for the fixed and random parameter estimates. Closed form local influence measures also allow them to assess the joint influence of various observations. They suggest a simple computation method and illustrate their results using two examples. Etude de I'influence locale dans les modeles multi-niveaux Les auteurs etudient l'influence locale des observations dans les modeles de regression multi-niveaux. A cette fin, ils perturbent a la fois les variances, les variables endogenes et la matrice d'incidence. Pour mesurer le changement local cause par ces perturbations, ils se servent des statistiques de Cook generalisees associees aux estimations des effets fixes et aleatoires. Des formules explicites leur permettent aussi de mesurer l'influence locale conjuguee de diverses observations. Ils suggerent une methode de calcul simple et illustrent leurs resultats a l'aide de deux exemples.
- Published
- 2008
24. Testing Serial Correlation in Partial Linear Errors-in-Variables Models Based on Empirical Likelihood
- Author
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Min Chen, Feng Liu, and Gemai Chen
- Subjects
Statistics and Probability ,Score test ,Empirical likelihood ,Autocorrelation ,Statistics ,Nonparametric statistics ,Linear model ,Chi-square test ,Errors-in-variables models ,Statistical hypothesis testing ,Mathematics - Abstract
In this article, we propose an empirical likelihood-based test to check the existence of serial correlation in partial linear errors-in-variables models. A nonparametric version of Wilk' theorem is derived, which says that our proposed test has an asymptotic chi-square distribution. Simulation results reveal that the finite sample performance of our proposed test is satisfactory in both size and power.
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- 2008
25. A new quantile function based model for modeling price behaviors in financial markets
- Author
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Gemai Chen, Zhenyu Wu, and Wenjiang Jiang
- Subjects
Statistics and Probability ,Applied Mathematics ,Financial market ,Econometrics ,Economics ,Quantile function - Published
- 2008
26. On inference for a semiparametric partially linear regression model with serially correlated errors
- Author
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Gemai Chen and Jinhong You
- Subjects
Statistics and Probability ,Goodness of fit ,Statistics ,Covariate ,Linear regression ,Nonparametric statistics ,Estimator ,Generalized least squares ,Semiparametric regression ,Statistics, Probability and Uncertainty ,Mathematics ,Parametric statistics - Abstract
The authors consider a semiparametric partially linear regression model with serially correlated errors. They propose a new way of estimating the error structure which has the advantage that it does not involve any nonparametric estimation. This allows them to develop an inference procedure consisting of a bandwidth selection method, an efficient semiparametric generalized least squares estimator of the parametric component, a goodness-of-fit test based on the bootstrap, and a technique for selecting significant covariates in the parametric component. They assess their approach through simulation studies and illustrate it with a concrete application. L'inference dans le cadre d'un modele de regression semiparametrique partiellement lineaire a termes d'erreur correles en serie Les auteurs s'interessent a un modele de regression semiparametrique partiellement lineaire a termes d'erreur correles en serie. Ils proposent une facon originale d'estimer la structure d'erreur qui a l'avantage de ne faire intervenir aucune estimation non parametrique. Ceci leur permet de developper une procedure d'inference comportant un choix de fenětre, l'emploi de la methode des moindres carres generalises pour l'estimation semiparametrique efficace de la composante parametrique, un test d'adequation fonde sur le reechantillonnage et une technique de selection des covariables significatives de la composante parametrique. Ils evaluent leur approche par voie de simulation et en donnent une illustration concrete.
- Published
- 2007
27. Statistical inference of partially linear regression models with heteroscedastic errors
- Author
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Yong Zhou, Gemai Chen, and Jinhong You
- Subjects
Statistics and Probability ,Heteroscedasticity ,Statistics::Theory ,Numerical Analysis ,Statistics::Applications ,Nonparametric statistics ,Linear model ,Model selection ,Local polynomial ,Semiparametric model ,Goodness of fit ,Statistics ,Econometrics ,Asymptotic normality ,Statistics::Methodology ,Semiparametric regression ,Semiparametric regression model ,Statistics, Probability and Uncertainty ,Park test ,Variance function ,Mathematics - Abstract
The authors study a heteroscedastic partially linear regression model and develop an inferential procedure for it. This includes a test of heteroscedasticity, a two-step estimator of the heteroscedastic variance function, semiparametric generalized least-squares estimators of the parametric and nonparametric components of the model, and a bootstrap goodness of fit test to see whether the nonparametric component can be parametrized.
- Published
- 2007
- Full Text
- View/download PDF
28. Graphing Kendall's
- Author
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Gemai Chen and Matthew K. Davis
- Subjects
Statistics and Probability ,Applied Mathematics ,Statistical computation ,Kendall s ,Measure (mathematics) ,Algebra ,Correlation ,Computational Mathematics ,Computational Theory and Mathematics ,Correlation analysis ,Calculus ,Graphics ,Word (computer architecture) ,Mathematics - Abstract
Correlation is an important and widely used concept, and it is usually taught through word explanation or graphic description accompanied with a numeric measure if such a measure exists. In this note, we explore graphing one of the commonly used correlation measures, Kendall's @t, in such a way that we display how Kendall's @t is calculated and see how Kendall's @t is influenced by data features.
- Published
- 2007
29. Semiparametric generalized least squares estimation in partially linear regression models with correlated errors
- Author
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Gemai Chen and Jinhong You
- Subjects
Statistics and Probability ,Applied Mathematics ,Statistics ,Ordinary least squares ,Semiparametric regression ,Generalized least squares ,Statistics, Probability and Uncertainty ,Total least squares ,Newey–West estimator ,Least squares ,Linear least squares ,Mathematics ,Variance function - Abstract
This paper is concerned with the estimation problem in partially linear regression models with serially correlated errors. The authors propose a semiparametric generalized least squares estimator (SGLSE) for the parametric component and show that it is asymptotically more efficient than the semiparametric ordinary least squares estimator (SOLSE) in terms of asymptotic covariance matrix. Other properties of this SGLSE including the asymptotic normality and the law of the iterated logarithm are established as well. A simulation study is conducted to examine the finite-sample properties of the proposed estimator and an empirical example is discussed.
- Published
- 2007
30. A New Hybrid Estimation Method for the Generalized Pareto Distribution
- Author
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Gemai Chen and Chunlin Wang
- Subjects
Statistics and Probability ,Mathematical optimization ,Bayes estimator ,021103 operations research ,Estimation theory ,0211 other engineering and technologies ,02 engineering and technology ,Trimmed estimator ,Maximum likelihood sequence estimation ,01 natural sciences ,Measure (mathematics) ,010104 statistics & probability ,Generalized Pareto distribution ,0101 mathematics ,Computational problem ,Extreme value theory ,Mathematics - Abstract
The generalized Pareto distribution (GPD) is important in the analysis of extreme values, especially in modeling exceedances over thresholds. Most of the existing methods for estimating the scale and shape parameters of the GPD suffer from theoretical and/or computational problems. A new hybrid estimation method is proposed in this article, which minimizes a goodness-of-fit measure and incorporates some useful likelihood information. Compared with the maximum likelihood method and other leading methods, our new hybrid estimation method retains high efficiency, reduces the estimation bias, and is computation friendly.
- Published
- 2015
- Full Text
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31. Hierarchical linear regression models for conditional quantiles
- Author
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Gemai Chen and Maozai Tian
- Subjects
Overdispersion ,General Mathematics ,Linear regression ,Outlier ,Statistics ,Econometrics ,Marginal model ,Random effects model ,Hierarchical database model ,Quantile regression ,Mathematics ,Quantile - Abstract
The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models, but it cannot deal effectively with the data with a hierarchical structure. In practice, the existence of such data hierarchies is neither accidental nor ignorable, it is a common phenomenon. To ignore this hierarchical data structure risks overlooking the importance of group effects, and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid. On the other hand, the hierarchical models take a hierarchical data structure into account and have also many applications in statistics, ranging from overdispersion to constructing min-max estimators. However, the hierarchical models are virtually the mean regression, therefore, they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates. Furthermore, the estimated coefficient vector (marginal effects) is sensitive to an outlier observation on the dependent variable. In this article, a new approach, which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models, is developed. On the theoretical front, we also consider the asymptotic properties of the new method, obtaining the simple conditions for an n1/2-convergence and an asymptotic normality. We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.
- Published
- 2006
32. Corrected local polynomial estimation in varying-coefficient models with measurement errors
- Author
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Gemai Chen, Jinhong You, and Yong Zhou
- Subjects
Statistics and Probability ,Goodness of fit ,Covariate ,Consistent estimator ,Statistics ,Asymptotic distribution ,Errors-in-variables models ,Estimator ,Regression analysis ,Statistics, Probability and Uncertainty ,Correction for attenuation ,Mathematics - Abstract
The authors study a varying-coefficient regression model in which some of the covariates are measured with additive errors. They find that the usual local linear estimator (LLE) of the coefficient functions is biased and that the usual correction for attenuation fails to work. They propose a corrected LLE and show that it is consistent and asymptotically normal, and they also construct a consistent estimator for the model error variance. They then extend the generalized likelihood technique to develop a goodness of fit test for the model. They evaluate these various procedures through simulation studies and use them to analyze data from the Framingham Heart Study. Estimation polynomiale locale corrigee dans les modeles a coefficients variables comportant des erreurs de mesure Les auteurs s'interessent a un modele de regression a coefficients variables dont certaines cova-riables sont entachees d'erreurs additives. Ils montrent que l'estimateur localement lineaire (ELL) usuel des coefficients fonctionnels est biaise et que le facteur de correction habituel du phenomene d'attenuation est inefficace. Ils proposent une version corrigee de l'ELL qui s'avere convergente et asymptotiquement normale; ils suggerent aussi une estimation convergente de la variance du terme d'erreur du modele. Une adaptation de la technique de vraisemblance generalisee leur permet en outre d'elaborer un test d'adequation du modele. Ils evaluent ces diverses procedures par voie de simulation et s'en servent pour analyser des donnees issues de l'etude Framingham sur les risques cardiometaboliques.
- Published
- 2006
33. A class of partially linear single-index survival models
- Author
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Gemai Chen, Xuewen Lu, Radhey S. Singh, and Peter X.-K. Song
- Subjects
Statistics and Probability ,Class (set theory) ,Proportional hazards regression ,Asymptotic distribution theory ,Statistics ,Asymptotic distribution ,Applied mathematics ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
The authors define a class of "partially linear single-index" survival models that are more flexible than the classical proportional hazards regression models in their treatment of covariates. The latter enter the proposed model either via a parametric linear form or a nonparametric single-index form. It is then pos sible to model both linear and functional effects of covariates on the logarithm of the hazard function and if necessary, to reduce the dimensionality of multiple covariates via the single-index component. The par tially linear hazards model and the single-index hazards model are special cases of the proposed model. The authors develop a likelihood-based inference to estimate the model components via an iterative algorithm. They establish an asymptotic distribution theory for the proposed estimators, examine their finite-sample behaviour through simulation, and use a set of real data to illustrate their approach. Une classe de modeles de survie partiellement lineaires a indice simple Rgsum=: Les auteurs d6finissent une classe de modeles de survie dits "partiellement lineaires a indice simple" qui s'averent plus flexibles que les modeles de regression a risques proportionnels classiques dans le traitement des covariables. Ces dernieres entrent dans le modele propose soit sous une forme lin6aire param6trique, soit sous une forme a indice simple non parametrique. I1 est alors possible de modeliser a la fois des effets lineaires et fonctionnels de covariables sur le logarithme du risque, et de reduire au besoin la dimension de covariables multiples par l'intermediaire de la composante a indice simple. Les modeles a risques partiellement lineaires et a indice simple sont des cas speciaux du modele propose. Les auteurs developpent une methode d'inf6rence vraisemblantiste pour l'estimation des composantes du modele au moyen d'un algorithme it6ratif. Ils d6terminent la loi asymptotique des estimateurs proposes, en etudient le comportement a taille finie par voie de simulation et illustrent leur approche a l'aide de donnees reelles.
- Published
- 2006
34. Block empirical likelihood for longitudinal partially linear regression models
- Author
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Jinhong You, Yong Zhou, and Gemai Chen
- Subjects
Statistics and Probability ,Progesterone level ,Empirical likelihood ,Statistics ,Linear regression ,Consistent estimator ,Nonparametric statistics ,Block (permutation group theory) ,Applied mathematics ,Statistics, Probability and Uncertainty ,Regression ,Confidence region ,Mathematics - Abstract
The authors propose a block empirical likelihood procedure to accommodate the within-group correlation in longitudinal partially linear regression models. This leads them to prove a nonparametric version of the Wilks theorem. In comparison with normal approximations, their method does not require a consistent estimator for the asymptotic covariance matrix, which makes it easier to conduct inference on the parametric component of the model. An application to a longitudinal study on fluctuations of progesterone level in a menstrual cycle is used to illustrate the procedure developed here. Une vraisemblance empirique par bloc pour les modeles de regression partiellernent lineaires longitudinaux Les auteurs proposent une procedure a base de vraisemblance empirique par bloc pour tenir compte de la correlation intra-groupe dans des modeles de regression partiellement lineaires longitudinaux. Ceci les ameneo a demontrer une version non parametrique du theoreme de Wilks. A la difference des approximations normales, leur methode ne fait pas appel a un estimateur convergent de la matrice des cova-riances asymptotiques, ce qui facilite l'inference concernant la composante parametrique du modele. Une etude longitudinale sur la fluctuation du niveau de progesterone pendant le cycle menstruel sert a illustrer le propos.
- Published
- 2006
35. Wild bootstrap estimation in partially linear models with heteroscedasticity
- Author
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Jinhong You and Gemai Chen
- Subjects
Statistics and Probability ,Statistics::Theory ,Heteroscedasticity ,Covariance matrix ,Linear model ,Estimator ,Asymptotic distribution ,Probability theory ,Consistent estimator ,Statistics ,Linear regression ,Statistics::Methodology ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
This paper uses the wild bootstrap technique in the estimation of a heteroscedastic partially linear regression model. We show that this approach provides reliable approximation to the asymptotic distribution of the semiparametric least-square estimators of the linear regression coefficients and consistent estimators of the asymptotic covariance matrices even when the error variances are unequal. In comparison, this robustness property is not shared by the bootstrap estimation proposed in Liang et al. (2000. Bootstrap approximation in a partially linear regression model. J. Statist. Plann. Inference, 91, 413–426).
- Published
- 2006
36. β -Spline Estimation in a Semiparametric Regression Model with Nonlinear Time Series Errors
- Author
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Xian Zhou, Jinhong You, and Gemai Chen
- Subjects
Statistics::Theory ,Multidisciplinary ,Generalized least squares ,Newey–West estimator ,Semiparametric model ,Statistics ,Ordinary least squares ,Statistics::Methodology ,Applied mathematics ,Semiparametric regression ,Total least squares ,Linear least squares ,Mathematics ,Variance function - Abstract
We study the estimation problems for a partly linear regression model with a nonlinear time series error structure. The model consists of a parametric linear component for the regression coefficients and a nonparametric nonlinear component. The random errors are unobservable and modeled by a first-order Markov bilinear process. Based on a B-spline series approximation of the nonlinear component function, we propose a semiparametric ordinary least squares estimator and a semiparametric generalized least squares estimator of the regression coefficients, a least squares estimator of the autoregression parameter for the errors, and a B-spline series estimator of the nonparametric component function. The asymptotic properties of these estimators are investigated and their asymptotic distributions are derived. We also provide a consistent estimator for the asymptotic covariance matrix of the semiparametric generalized least squares estimator of the regression coefficients. Our results can be used to make asymptotically efficient statistical inferences. In addition, a small simulation is conducted to evaluate the performance of the proposed estimators, which shows that the semiparametric generalized least squares estimator of the regression coefficients is more efficient than the semiparametric ordinary least squares estimator.
- Published
- 2005
37. Testing heteroscedasticity in partially linear regression models
- Author
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Gemai Chen and Jinhong You
- Subjects
Statistics and Probability ,Heteroscedasticity ,Proper linear model ,Homoscedasticity ,Linear regression ,Statistics ,Econometrics ,Asymptotic distribution ,Regression analysis ,Statistics, Probability and Uncertainty ,Park test ,Mathematics ,Statistical hypothesis testing - Abstract
Efficient inference for regression models requires that heteroscedasticity be taken into account if it exists. For partially linear regression models, however, the problem of detecting heteroscedasticity has received very little attention. The aim of this paper is to propose a test of heteroscedasticity for partially linear regression models.
- Published
- 2005
38. Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models
- Author
-
Gemai Chen and Jinhong You
- Subjects
Iteratively reweighted least squares ,Applied Mathematics ,Non-linear least squares ,Statistics ,Generalized least squares ,Semiparametric regression ,Total least squares ,Least squares ,Linear least squares ,Mathematics ,Variance function - Abstract
Consider a repeated measurement partially linear regression model with an unknown vector parameter β 1, an unknown function g(·), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.
- Published
- 2005
39. An asymptotic theory for semiparametric generalized least squares estimation in partially linear regression models
- Author
-
Jinhong You and Gemai Chen
- Subjects
Statistics and Probability ,Statistics::Theory ,Explained sum of squares ,Generalized least squares ,Least squares ,Non-linear least squares ,Statistics ,Applied mathematics ,Semiparametric regression ,Statistics, Probability and Uncertainty ,Total least squares ,Linear least squares ,Mathematics ,Variance function - Abstract
Consider a partially linear regression model with an unknown vector parameter β, an unknown functiong(·), and unknown heteroscedastic error variances. In this paper we develop an asymptotic semiparametric generalized least squares estimation theory under some weak moment conditions. These moment conditions are satisfied by many of the error distributions encountered in practice, and our theory does not require the number of replications to go to infinity.
- Published
- 2005
40. A New Multivariate Control Chart for Monitoring Both Location and Dispersion
- Author
-
Smiley W. Cheng, Gemai Chen, and Hansheng Xie
- Subjects
ComputingMilieux_GENERAL ,Statistics and Probability ,Motion chart ,u-chart ,Chart ,Control limits ,Modeling and Simulation ,Statistics ,X-bar chart ,Radar chart ,EWMA chart ,Shewhart individuals control chart ,Mathematics - Abstract
A multivariate exponentially weighted moving average single control chart is developed in this article. This chart is capable of monitoring simultaneously the process mean vector and the process covariance matrix. Our average run length comparison shows that this new chart performs better than the combination of the χ2 chart and the |S| chart when small changes in the process parameters are of interest.
- Published
- 2005
41. An Extended EWMA Mean Chart
- Author
-
Lingyun Zhang and Gemai Chen
- Subjects
Information Systems and Management ,Chart ,Average run length ,Management of Technology and Innovation ,Industrial relations ,Statistics ,Exponentially weighted moving average ,Ranging ,EWMA chart ,Management Science and Operations Research ,Business and International Management ,Standard deviation ,Mathematics - Abstract
In this paper, we extend the exponentially weighted moving average (EWMA) technique to double exponentially weighted moving average (DEWMA) technique. We show that DEWMA mean charts perform better than EWMA mean charts in detecting small mean shifts ranging from 0.1 to 0.5 of the process standard deviation, and that the two types of charts perform similarly when mean shifts are larger than 0.5 standard deviation. The design of DEWMA mean charts is also discussed.
- Published
- 2005
42. Block external bootstrap in partially linear models with nonstationary strong mixing error terms
- Author
-
Jinhong You and Gemai Chen
- Subjects
Statistics and Probability ,Combinatorics ,Matrix (mathematics) ,Distribution (mathematics) ,Linear regression ,Consistent estimator ,Linear model ,Estimator ,Applied mathematics ,Statistics, Probability and Uncertainty ,Covariance ,Mathematics ,Parametric statistics - Abstract
The authors extend the block external bootstrap to partially linear regression models with strongly mixing, nonstationary error terms. In addition to providing an approximate distribution for the semiparametric least square estimator of the parametric component, they propose a consistent estimator of the co-variance matrix of this estimator. Les auteurs etendent le bootstrap externe par bloc aux modeles partiellement lineaires dont les termes d'erreur sont fortement melangeants et non stationnaires. En plus de donner une approximation de la loi de l'estimateur des moindres carres semiparametrique de la composante parametrique, ils proposent un estimateur convergent de la matrice de covariance de cet estimateur.
- Published
- 2004
43. Tests of transformation in nonlinear regression
- Author
-
Gemai Chen and Zhenlin Yang
- Subjects
Hessian matrix ,Score test ,Economics and Econometrics ,Mathematical optimization ,Power transform ,symbols.namesake ,Transformation (function) ,Lagrange multiplier ,Non-linear least squares ,symbols ,Applied mathematics ,Nonlinear regression ,Finance ,Mathematics - Abstract
This paper presents three versions of the Lagrange multiplier (LM) tests of transformation in nonlinear regression: (i) LM test based on expected information, (ii) LM test based on Hessian, and (iii) the LM test based on gradient. All three tests can be easily implemented through a nonlinear least squares procedure. Simulation results show that, in terms of finite sample performance, the LM test based on expected information is the best, followed by the LM test based on Hessian and then the LM test based on gradient. The LM test based on gradient can perform rather poorly. An example is given for illustration.
- Published
- 2004
44. EWMA Charts for Monitoring the Mean of Censored Weibull Lifetimes
- Author
-
Lingyun Zhang and Gemai Chen
- Subjects
021103 operations research ,Strategy and Management ,0211 other engineering and technologies ,Exponentially weighted moving average ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Censoring (statistics) ,Industrial and Manufacturing Engineering ,010104 statistics & probability ,Statistics ,Econometrics ,EWMA chart ,0101 mathematics ,Safety, Risk, Reliability and Quality ,Mathematics ,Weibull distribution - Abstract
Lower-sided and upper-sided exponentially weighted moving average (EWMA) charts are developed for detecting mean changes when censoring occurs at a fixed level in processes characterized by Weibull distributions. The lower-sided EWMA chart performs bett..
- Published
- 2004
45. Millennial-scale relationships of diatom species richness and production in two prairie lakes
- Author
-
Olaf Olson, Suzanne McGowan, James A. Rusak, Gemai Chen, Peter R. Leavitt, Brian F. Cumming, and Sybille Wunsam
- Subjects
Abiotic component ,Biogeochemical cycle ,Diatom ,biology ,Algae ,Ecology ,Stable isotope ratio ,Biodiversity ,Ecosystem ,Species richness ,Aquatic Science ,Oceanography ,biology.organism_classification - Abstract
Insight into the causes and consequences of changes in aquatic biodiversity requires an improved understanding of the nature of the relationships between species richness and ecosystem function over a much longer temporal perspective than we currently possess. We used high-resolution paleoecological records from two prairie lakes to show that diatom species richness (as fossil frustules) was negatively correlated ( r 2 5 0.09‐0.24, p , 0.001) with diatom production (as fossil pigments) during the past 2,000 yr. By comparing analyses from intervals of fresh and saline waters, we demonstrate that these significant richness‐production relationships arose during freshwater periods (r 2 5 0.13‐0.45, p , 0.001) and could be eliminated (r 2 , 0.02, p . 0.1) by abiotic disturbances such as droughts. Procrustes analyses of the concordance of species change within freshwater communities and the change in richness‐ production relationships through time revealed that shifts in diatom community composition could have a large influence in determining the negative relationship between richness and production. Finally, significant correlations (r 2 5 0.09‐0.24, p , 0.0001) between past diatom species richness and ratios of stable isotopes (primarily d 15 N) suggested that C and N biogeochemical cycles are also linked to changes in algal biodiversity. Taken together, these analyses suggest that the ongoing disruption of climate and biogeochemical systems by humans may obscure the relationship between aquatic biodiversity and ecosystem function in the future.
- Published
- 2004
46. Computing Average Run Lengths for the MaxEWMA Chart
- Author
-
Maria E. Calzada, Gemai Chen, and Stephen M. Scariano
- Subjects
Statistics and Probability ,Mean estimation ,Chart ,Computer simulation ,Average run length ,Modeling and Simulation ,Statistics ,Process (computing) ,Control chart ,EWMA chart ,Standard deviation ,Mathematics - Abstract
The MaxEWMA chart has recently been introduced as an alternative to control charting procedures that are designed to jointly detect changes in the mean and standard deviation of a normally distributed process. Here, a method for computing both in-control and out-of-control average run lengths for purposes of effectively designing this chart is offered. Design strategies are considered, numerical results to aid the design effort are given, and examples are discussed.
- Published
- 2004
47. A New EWMA Control Chart for Monitoring Both Location and Dispersion
- Author
-
Gemai Chen, Smiley W. Cheng, and Hansheng Xie
- Subjects
Information Systems and Management ,Computer science ,X-bar chart ,Process (computing) ,Management Science and Operations Research ,Chart ,Management of Technology and Innovation ,Industrial relations ,Statistics ,Statistical dispersion ,Control chart ,EWMA chart ,Business and International Management ,Process variability ,Algorithm ,Statistic - Abstract
A new control chart, which employs the exponentially weighted moving average (EWMA) technique, is proposed. The statistic for the chart defines the area below a straight line as the control region, which makes the charting procedure easier than the usual approach. This chart can effectively monitor the process mean and the increased process variability simultaneously, and can detect the source and the direction of a change easily.
- Published
- 2004
48. Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity
- Author
-
Gemai Chen and Jinhong You
- Subjects
Delta method ,Heteroscedasticity ,Applied Mathematics ,Statistics ,Ordinary least squares ,Consistent estimator ,Estimator ,Generalized least squares ,Newey–West estimator ,Jackknife resampling ,Mathematics - Abstract
Consider a partially linear regression model with an unknown vector parameter β, an unknown function g(·), and unknown heteroscedastic error variances. Chen, You[23] proposed a semiparametric generalized least squares estimator (SGLSE) for β, which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].
- Published
- 2003
49. Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors
- Author
-
Min Chen, Jin-hong You, Xue-lei Jiang, and Gemai Chen
- Subjects
Combinatorics ,Zero mean ,Compact space ,Applied Mathematics ,Uniform convergence ,Linear regression ,Statistics ,Order (ring theory) ,Arma process ,Real line ,Random variable ,Mathematics - Abstract
Consider the partly linear regression model $$ y_{i} = {x}'_{i} \beta + g{\left( {t_{i} } \right)} + \varepsilon _{i} ,\;\;{\kern 1pt} 1 \leqslant i \leqslant n $$ , where y i ’s are responses, $$ x_{i} = {\left( {x_{{i1}} ,x_{{i2}} , \cdots ,x_{{ip}} } \right)}^{\prime } \;\;\;{\text{and}}\;\;\;t_{i} \in {\cal T} $$ are known and nonrandom design points, $$ {\cal T} $$ is a compact set in the real line $$ {\cal R} $$ , β = (β 1, ··· , β p )' is an unknown parameter vector, g(·) is an unknown function and {e i } is a linear process, i.e., $$ \varepsilon _{i} {\kern 1pt} = {\kern 1pt} {\sum\limits_{j = 0}^\infty {\psi _{j} e_{{i - j}} ,{\kern 1pt} \;\psi _{0} {\kern 1pt} = {\kern 1pt} 1,\;{\kern 1pt} {\sum\limits_{j = 0}^\infty {{\left| {\psi _{j} } \right|} < \infty } }} } $$ , where e j are i.i.d. random variables with zero mean and variance $$ \sigma ^{2}_{e} $$ . Drawing upon B-spline estimation of g(·) and least squares estimation of β, we construct estimators of the autocovariances of {e i }. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {e i } are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process.
- Published
- 2003
50. Jackknife Estimation for Smooth Functions of the Parametric Component in Partially Linear Regression Models
- Author
-
Jinhong You and Gemai Chen
- Subjects
Statistics and Probability ,Delta method ,Extremum estimator ,Consistent estimator ,Statistics ,Linear model ,Nonparametric statistics ,Asymptotic distribution ,Estimator ,Jackknife resampling ,Mathematics - Abstract
It is known that due to the existence of the nonparametric component, the usual estimators for the parametric component or its function in partially linear regression models are biased. Sometimes this bias is severe. To reduce the bias, we propose two jackknife estimators and compare them with the naive estimator. All three estimators are shown to be asymptotically equivalent and asymptotically normally distributed under some regularity conditions. However, through simulation we demonstrate that the jackknife estimators perform better than the naive estimator in terms of bias when the sample size is small to moderate. To make our results more useful, we also construct consistent estimators of the asymptotic variance, which are robust against heterogeneity of the error variances.
- Published
- 2003
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