84 results on '"Gemai Chen"'
Search Results
52. Box-Cox transformations in linear models: Large sample theory and tests of normality
- Author
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Michael A. Stephens, Gemai Chen, and Richard A. Lockhart
- Subjects
Statistics and Probability ,Local asymptotic normality ,media_common.quotation_subject ,Linear model ,Estimator ,Empirical distribution function ,Standard error ,Goodness of fit ,Statistics ,Linear regression ,Applied mathematics ,Statistics, Probability and Uncertainty ,Normality ,Mathematics ,media_common - Abstract
The authors provide a rigorous large sample theory for linear models whose response variable has been subjected to the Box-Cox transformation. They provide a continuous asymptotic approximation to the distribution of estimators of natural parameters of the model. They show, in particular, that the maximum likelihood estimator of the ratio of slope to residual standard deviation is consistent and relatively stable. The authors further show the importance for inference of normality of the errors and give tests for normality based on the estimated residuals. For non-normal errors, they give adjustments to the log-likelihood and to asymptotic standard errors.
- Published
- 2002
53. A NOTE ON EWMA CHARTS FOR MONITORING MEAN CHANGES IN NORMAL PROCESSES
- Author
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Gemai Chen and Lingyun Zhang
- Subjects
Statistics and Probability ,symbols.namesake ,Efficient estimator ,Chart ,Moving average ,Control limits ,Statistics ,symbols ,Control chart ,Variance (accounting) ,EWMA chart ,Gaussian process ,Mathematics - Abstract
We prove that the standard EWMA mean chart with asymptotic control limits and the EWMA mean chart with time-varying control limits for monitoring mean changes in a normal process with known mean and known variance are ARL-unbiased. Using the results derived we discuss the effects of estimation of the process mean on ARL.
- Published
- 2002
54. Theory & Methods: On a Class of Nonlinear AR( P ) Models with Nonlinear ARCH Errors
- Author
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Min Chen and Gemai Chen
- Subjects
Statistics and Probability ,Class (set theory) ,Nonlinear system ,Series (mathematics) ,Autoregressive model ,Mathematical analysis ,Ergodicity ,Statistics, Probability and Uncertainty ,Arch ,Mathematics - Abstract
This paper studies general sufficient conditions for the geometric ergodicity and the existence of moments for a class of nonlinear autoregressive models with nonlinear ARCH errors. Applications of these conditions to various well-known nonlinear time series models yield specific sufficient conditions, many of which are new or generalizations of existing conditions.
- Published
- 2001
55. A nonparametric test of conditional autoregressive heteroscedasticity for threshold autoregressive models
- Author
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Gemai Chen and Min Chen
- Subjects
Statistics and Probability ,Statistics::Theory ,Heteroscedasticity ,Nonlinear autoregressive exogenous model ,Statistics::Applications ,Autoregressive conditional heteroskedasticity ,Nonparametric statistics ,SETAR ,Autoregressive model ,Statistics ,Econometrics ,Statistics::Methodology ,Statistics, Probability and Uncertainty ,Conditional variance ,STAR model ,Mathematics - Abstract
Threshold autoregressive models are widely used in time-series applications. When building or using such a model, it is important to know whether conditional heteroscedasticity exists. The authors propose a nonparametric test of this hypothesis. They develop the large-sample theory of a test of nonlinear conditional heteroscedasticity adapted to nonlinear autoregressive models and study its finite-sample properties through simulations. They also provide percentage points for carrying out this test, which is found to have very good power overall.
- Published
- 2001
56. Monitoring Process Mean and Variability with One EWMA Chart
- Author
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Hansheng Xie, Gemai Chen, and Smiley W. Cheng
- Subjects
021103 operations research ,Average run length ,Computer science ,Strategy and Management ,0211 other engineering and technologies ,Process (computing) ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Industrial and Manufacturing Engineering ,ComputingMilieux_GENERAL ,010104 statistics & probability ,Chart ,Statistics ,Control chart ,EWMA chart ,0101 mathematics ,Safety, Risk, Reliability and Quality - Abstract
Two EWMA charts are usually required to monitor both process mean and variability. In this paper, we propose a new EWMA chart which effectively combines the usual two EWMA charts into one chart. In...
- Published
- 2001
57. Application of a Least Square Non-parametric Discovery Process Model to Colorado Group Mixed Conventional and Unconventional Oil Plays, Western Canada Sedimentary Basin
- Author
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Zhuoheng Chen, Gemai Chen, and Kirk G. Osadetz
- Subjects
geography ,geography.geographical_feature_category ,Resource (biology) ,organic chemicals ,technology, industry, and agriculture ,Geochemistry ,Unconventional oil ,Sedimentary basin ,Petroleum play ,complex mixtures ,Least squares ,Business process discovery ,chemistry.chemical_compound ,Mining engineering ,chemistry ,Group (stratigraphy) ,Petroleum ,lipids (amino acids, peptides, and proteins) ,Geology - Abstract
A least squares non-parametric discovery process model has been developed recently for assessing petroleum resources in mature plays with complex size distribution characteristics. Applications of this model to oil plays in the Colorado Group suggests that these techniques can be used to assess petroleum plays composed of a mixture of pools comprising both conventional and unconventional petroleum accumulations. We use the Cardium oil play of the Colorado Group in the Western Canada Sedimentary Basin to illustrate use of the non-parametric approach for such a mixed petroleum play. Our Colorado Group resource assessment indicates a large remaining oil resource potential in this petroleum system, largely in tight unconventional reservoirs.
- Published
- 2013
58. Geometric ergodicity of nonlinear autoregressive models with changing conditional variances
- Author
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Gemai Chen and Min Chen
- Subjects
Statistics and Probability ,Combinatorics ,Independent and identically distributed random variables ,Nonlinear system ,Mixing (mathematics) ,Autoregressive model ,Stochastic process ,Ergodicity ,Statistics ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
The authors give easy-to-check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random process xt = ϕ(xt-1,…, xt-p) + ϵtσ(xt-1,…, xt-q) in which ϕ: Rp R, σ Rq R and (ϵt) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)-ARCH(p), and the double-threshold autoregressive models. Les auteurs enoncent des conditions faciles a verifier qui garantissent l'ergodicite geometrique et la finitude des moments d'un processus aleatoire xt = ϵ(xt-1,…, xt-p) + ϵtσ(xt-1,…, xt-q) defini a partir de fonctions ϕ: Rp R, σ: Rq R et d'une suite (ϵt) d'aleas independants de měme loi. Ils en deduisent des proprietes de melangeance forte pour cette classe de modeles autoregressifs non lineaires a variances conditionnelles variables qui englobe, entre autres, les modeles ARCH(p), les modeles AR(p)-ARCH(p), ainsi que les modeles autoregressifs a double seuil.
- Published
- 2000
59. Influence Measures for General Linear Models With Correlated Errors
- Author
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Lei Shi and Gemai Chen
- Subjects
Statistics and Probability ,Generalized linear model ,Hierarchical generalized linear model ,General linear model ,Proper linear model ,General Mathematics ,Linear regression ,Statistics ,Leverage (statistics) ,Statistics, Probability and Uncertainty ,Cook's distance ,Generalized linear mixed model ,Mathematics - Abstract
We give simple and concise expressions of influence measures for general linear models with correlated errors. We show that the commonly used influence measures can be expressed as functions of the generalized leverages and residuals and have the same forms as those in standard linear regression models.
- Published
- 2009
60. An ImprovedpChart Through Simple Adjustments
- Author
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Gemai Chen
- Subjects
Strategy and Management ,X-bar chart ,Normal values ,Management Science and Operations Research ,Industrial and Manufacturing Engineering ,Large sample ,Binomial distribution ,Statistics ,Control chart ,Fraction (mathematics) ,False alarm ,Safety, Risk, Reliability and Quality ,p-chart ,Mathematics - Abstract
The p chart for monitoring the fraction, p, of nonconforming products requires very large sample sizes to achieve any power in detecting decreases in p, and the false alarm for probabilities differ considerably from the nomial normal values. Two alterna..
- Published
- 1998
61. The exact u chart can be obtained using simple adjustments
- Author
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Smiley W. Cheng and Gemai Chen
- Subjects
Statistics and Probability ,u-chart ,Scale (ratio) ,X-bar chart ,Poisson distribution ,Cornish–Fisher expansion ,symbols.namesake ,Chart ,Control limits ,Statistics ,symbols ,False alarm ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
The u chart for monitoring λ, the average number of defects per inspection unit, requires λ to be large to have positive lower control limits, and the false alarm probabilities differ considerably from the nominal normal values. Based on nonlinear transformations, some alternative charts, such as the chart, can achieve large improvement over the u chart. We show in this paper that with very simple adjustments to the control limits of the u chart, one can achieve equal or even better improvement while still working on the original scale. In particular, using the very simple adjustments is equivalent to using the exact Poisson distribution to design a chart. Some guidelines for choosing an appropriate chart are given.
- Published
- 1998
62. Box-Cox transformed linear models: A parameter-based asymptotic approach
- Author
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Gemai Chen and Richard A. Lockhart
- Subjects
Statistics and Probability ,Combinatorics ,symbols.namesake ,Linear model ,Calculus ,symbols ,Statistics, Probability and Uncertainty ,Mathematics ,F-distribution - Abstract
A Box-Cox transformed linear model usually has the form y(λ) = μ + β1x1 +… + βpxp + oe, where y(λ) is the power transform of y. Although widely used in practice, the Fisher information matrix for the unknown parameters and, in particular, its inverse have not been studied seriously in the literature. We obtain those two important matrices to put the Box-Cox transformed linear model on a firmer ground. The question of how to make inference on β = (β1,…,βp)T when λ; is estimated from the data is then discussed for large but finite sample size by studying some parameter-based asymptotics. Both unconditional and conditional inference are studied from the frequentist point of view. Un modele lineaire transforme suivant Box-Cox a habituellement la forme y(λ) = μ+β1x1 +…+ βpxp + oϵ, ou y(λ) est est la transformation puissance de y. Malgre le fait qu'elle est communement utilisee dans la pratique, la matrice d'information de Fisher pour les parametres inconnus et, en particulier, son inverse n'ont pas ete etudiees serieusement dans la litterature. Dans cet article, nous obtenons ces deux importantes matrices ce qui permet de placer le modele lineaire transforme suivant Box-Cox sur des bases plus solides. Nous etudions I'inference au sujet de β = (β1,….βp)T lorsque λ est estime a partir des donnees, cela pour un echantillon fini de grande taille et en considerant certaines asymptotiques fondees sur des parametres. Nous etudions, d'un point de vue frequentiel, les inferences inconditionnelle et conditionnelle.
- Published
- 1997
63. PARAMETRIC AND NON-PARAMETRIC MODELLING OF TIME SERIES — AN EMPIRICAL STUDY
- Author
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Greg W. Bennett, Gemai Chen, and Bovas Abraham
- Subjects
Statistics and Probability ,Multivariate adaptive regression splines ,Computer science ,Ecological Modeling ,Parametric model ,Econometrics ,Nonparametric statistics ,Autoregressive integrated moving average ,Time series ,Algorithm ,Smoothing ,Nonparametric regression ,Parametric statistics - Abstract
Time series modelling methods can be loosely classified as (i) parametric methods and (ii) non-parametric methods. Within a usually quite flexible but well structured family of models, the parametric modelling process typically consists of model identification, parameter estimation, model diagnostic checking, and forecasting. On the other hand, within a much less structured framework, different non-parametric smoothing techniques are usually used to bring out the features of the observed time series, however, few serious and systematic attempts have been made to model time series non-parametrically. We concentrate on a non-parametric method based on multivariate adaptive regression splines (MARS). Parallel to the parametric modelling process, we systemize a non-parametric modelling process as (i) model perception (where a very large spline expansion of a very large family of models is specified), (ii) model search (forward plus backward search to come up with a model), (iii) model diagnostic checking, and (iv) forecasting. The major difference between the MARS and the parametric methods is that the potential models for the MARS method form a family which is much larger than any family of parametric time series models, and the local structures found in the data are used to guide the search for a fitted model. Also, unlike most non-parametric methods, MARS time series models can be analytically written down. In this paper, we present the results of an empirical comparison of parametric (ARIMA) and non-parametric (MARS) time series modelling methods. Eight environmental time series are used for the comparison. © 1997 by John Wiley & Sons Ltd.
- Published
- 1997
64. EDF tests of goodness of fit for transform-both-sides models
- Author
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Gemai Chen
- Subjects
Statistics and Probability ,Combinatorics ,Goodness of fit ,Statistics ,Statistics, Probability and Uncertainty ,Mathematics - Abstract
Very often in regression analysis, a particular functional form connecting known covariates and unknown parameters is either suggested by previous work or demanded by theoretical considerations so that the deterministic part of the responses has a known form. However, the underlying error structure is often less well understood. In this case, the transform-both-sides (TBS) models are appropriate. In this paper we generalize the usual TBS models and develop tests to assess goodness of fit when fitting TBS or GTBS models. Parameter estimation is discussed, and tests based on the Cramer-von Mises statistic and the Anderson-Darling statistic are presented with a table suitable for finite-sample applications. Tres souvent, lors de l'analyse de la regression, une forme fonctionnelle particuliere reliant des “covariates” connus et des parametres inconnus est soit suggeree par des travaux anterieurs, soit exigee par des considerations theoriques afin que la partie deterministe des reponses ait une forme connue. Toutefois, la structure d'erreur sous-jacente est souvent moins bien comprise. Dans ce cas, les modeles TBS (“transform-both-sides”) sont appropries. Cet article generalise les modeles TBS habituels et developpe des tests pour evaluer la validite de l'ajustement lorsqu'on ajuste des modeles TBS ou GTBS. Nous discutons l'estimation des parametres et presentons des tests fondes sur la statistique Cramer-von Mises et la statistique Anderson-Darling avec un tableaux convenant a des applications a echantillon fini.
- Published
- 1996
65. A General Purpose Approximate Goodness-of-Fit Test
- Author
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Narayanaswamy Balakrishnan and Gemai Chen
- Subjects
021103 operations research ,Strategy and Management ,media_common.quotation_subject ,Monte Carlo method ,0211 other engineering and technologies ,Sample (statistics) ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Industrial and Manufacturing Engineering ,Test (assessment) ,010104 statistics & probability ,Goodness of fit ,Statistics ,Econometrics ,Data analysis ,Quality (business) ,0101 mathematics ,Safety, Risk, Reliability and Quality ,Reliability (statistics) ,media_common ,Statistical hypothesis testing ,Mathematics - Abstract
Skewed distributions play an important role in the analysis of data from quality and reliability experiments. Very often unknown parameters must be estimated from the sample data in order to test whether the data has come from a certain family of distri..
- Published
- 1995
66. Generalized log-normal distributions with reliability application
- Author
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Gemai Chen
- Subjects
Statistics and Probability ,Scale (ratio) ,Estimation theory ,Applied Mathematics ,Statistical parameter ,Computational Mathematics ,Computational Theory and Mathematics ,Goodness of fit ,Statistics ,Gamma distribution ,Applied mathematics ,Scale parameter ,Mathematics ,K-distribution ,Weibull distribution - Abstract
A specific scale must be used to collect data in an experiment, but this scale may or may not be the appropriate scale to analyze the data thus collected. In this paper, we study a family of three-parameter distributions which includes the log-normal distribution as a special case, and one of the parameters plays the role of choosing a suitable scale for subsequent analysis. Some basic properties and maximum likelihood estimation of the unknown parameters are discussed, and an easy-to-use goodness-of-fit test is developed. A real data set, to which the usual Weibull, log-normal and gamma distributions cannot be fitted, is used to demonstrate the potential applicability of this family of distributions.
- Published
- 1995
67. LAG WINDOW ESTIMATION OF THE DEGREE OF DIFFERENCING IN FRACTIONALLY INTEGRATED TIME SERIES MODELS
- Author
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Shelton Peiris, Gemai Chen, and Bovas Abraham
- Subjects
Statistics and Probability ,Mean squared error ,Applied Mathematics ,Lag ,Estimator ,Lag operator ,Autoregressive model ,Statistics ,Range (statistics) ,Applied mathematics ,Statistics, Probability and Uncertainty ,Time series ,Autoregressive fractionally integrated moving average ,Mathematics - Abstract
In this paper we consider the estimation of the degree of differencing d in the fractionally integrated autoregressive moving-average time series model ARFIMA (p, d, q). Using lag window spectral density estimators we develop a regression type estimator of d which is easy to calculate and does not require prior knowledge of p and q. Some large sample properties of the estimator are studied and the performance of the estimator for small samples is investigated using the simulation method for a range of commonly used lag windows. Some practical recommendations on the choice of lag windows and the choice of the window parameters are provided.
- Published
- 1994
68. Some specific contiguous alternatives to the normal error assumption in linear models
- Author
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Gemai Chen
- Subjects
Statistics and Probability ,Weak convergence ,Linear model ,Residual ,Inverse Gaussian distribution ,Hierarchical generalized linear model ,symbols.namesake ,Goodness of fit ,Statistics ,symbols ,Gamma distribution ,Applied mathematics ,Statistics, Probability and Uncertainty ,Empirical process ,Mathematics - Abstract
Weak convergence results are obtained in this paper for the residual empirical processes in linear models, when the normal error assumption is replaced by a number of other error assumptions such as the Gamma family and the inverse Gaussian family. Application to asymptotic power calculations for a class of tests of fit is discussed.
- Published
- 1993
69. A New Distribution for Extreme Value Analysis
- Author
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Wenjiang Jiang, Chris Bunce, and Gemai Chen
- Subjects
Minimum distance estimation ,Generalized Pareto distribution ,Cumulative distribution function ,Statistics ,Generalized extreme value distribution ,Fréchet distribution ,Applied mathematics ,Quantile function ,Extreme value theory ,Shape parameter ,Mathematics - Abstract
The shape of the commonly used distributions in extreme value analysis is determined by either a specific functional form or a shape parameter. In this paper, we develop a family of distributions which uses two parameters to determine the shape: a balance parameter to control symmetry and a tail order parameter to control the thickness of the tail and modes. Each member in this family has closed forms for its density, cumulative distribution, and quantile function. We discuss the maximum likelihood and minimum distance estimation of the unknown parameters and illustrate the usefulness of the new distribution in extreme value analysis with a real data set.
- Published
- 2010
70. On t and EWMA t Charts for Monitoring Changes in the Process Mean
- Author
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Gemai Chen, Lingyun Zhang, Philippe Castagliola, Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), Mines Nantes (Mines Nantes)-École Centrale de Nantes (ECN)-Ecole Polytechnique de l'Université de Nantes (EPUN), and Université de Nantes (UN)-Université de Nantes (UN)-PRES Université Nantes Angers Le Mans (UNAM)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Engineering ,021103 operations research ,business.industry ,X-bar chart ,0211 other engineering and technologies ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,\bar x and s chart ,Standard deviation ,010104 statistics & probability ,Chart ,Control limits ,Statistics ,EWMA chart ,0101 mathematics ,Safety, Risk, Reliability and Quality ,Shewhart individuals control chart ,business ,\bar x and R chart ,ComputingMilieux_MISCELLANEOUS - Abstract
The performance of an X-bar chart is usually studied under the assumption that the process standard deviation is well estimated and does not change. This is, of course, not always the case in practice. We find that X-bar charts are not robust against errors in estimating the process standard deviation or changing standard deviation. In this paper we discuss the use of a t chart and an exponentially weighted moving average (EWMA) t chart to monitor the process mean. We determine the optimal control limits for the EWMA t chart and show that this chart has the desired robustness property. Copyright © 2009 John Wiley & Sons, Ltd.
- Published
- 2009
71. The Exact Run Length Distribution and Design of the S2 Chart when the In-Control Variance is Estimated
- Author
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Gemai Chen, Philippe Castagliola, Giovanni Celano, Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), Mines Nantes (Mines Nantes)-École Centrale de Nantes (ECN)-Ecole Polytechnique de l'Université de Nantes (EPUN), and Université de Nantes (UN)-Université de Nantes (UN)-PRES Université Nantes Angers Le Mans (UNAM)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
General Computer Science ,X-bar chart ,Energy Engineering and Power Technology ,Aerospace Engineering ,s2 control chart ,Variance (accounting) ,Conditional probability distribution ,Industrial and Manufacturing Engineering ,Standard deviation ,Process variance ,conditional distribution ,One-way analysis of variance ,Nuclear Energy and Engineering ,Chart ,Control limits ,Statistics ,Control chart ,Electrical and Electronic Engineering ,Safety, Risk, Reliability and Quality ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
When monitoring the process variability, it is a common practice that a Phase I data set is used to estimate the unknown in-control process standard deviation σ0 or variance [Formula: see text] to set up the control limits, then monitoring proceeds. Once the process is considered to be in-control, the estimated control limits are assumed as fixed. This practice ignores the effect of estimating the unknown in-control process variance [Formula: see text]. In this paper, we derive the exact run length distribution of the S2 control chart when the in-control process variance [Formula: see text] is estimated and find that m = 200 or more Phase I samples are needed to neglect the effect of using estimated control limits. New control limits when m is small are also derived.
- Published
- 2009
72. Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model
- Author
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Gemai Chen and Jinhong You
- Subjects
Polynomial regression ,Statistics and Probability ,Numerical Analysis ,Estimator ,Attenuation ,Generalized least squares ,Varying-coefficient ,Local polynomial ,Nonparametric regression ,Measurement error ,Convergence rate ,Consistent estimator ,Statistics ,Partially linear regression model ,Asymptotic normality ,Statistics::Methodology ,Semiparametric regression ,Simple linear regression ,Statistics, Probability and Uncertainty ,Variance function ,Mathematics - Abstract
This paper studies the estimation of a varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model [Fan and Huang, Manuscript, University of North Carolina, Chapel Hill, USA, 2002]. We focus on the case where some covariates are measured with additive errors. The usual profile least squares and local polynomial estimations lead to biased estimators of the parametric and nonparametric components, respectively, when measurement errors are ignored. By correcting the attenuation we propose a modified profile least squares estimator for the parametric component and a local polynomial estimator for the nonparametric component. We show that the former is consistent, asymptotically normal and achieves the rate in the law of the iterated logarithm, and the latter achieves the optimal strong convergence rate of the usual nonparametric regression. In addition, a consistent estimator is also developed for the error variance. These results can be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.
- Published
- 2006
- Full Text
- View/download PDF
73. Weak convergence of the empirical process of residuals in linear models with many parameters
- Author
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Gemai Chen and Richard A. Lockhart
- Subjects
62E20 ,Statistics and Probability ,empirical processes ,Weak convergence ,Mean squared error ,goodness-of-fit ,Linear model ,Residual ,Least squares ,Residual sum of squares ,Non-linear least squares ,Statistics ,Applied mathematics ,regression ,62J99 ,Statistics, Probability and Uncertainty ,Linear least squares ,Mathematics - Abstract
When fitting, by least squares, a linear model (with an intercept term) with $p$ parameters to $n$ data points, the asymptotic behavior of the residual empirical process is shown to be the same as in the single sample problem provided $p^3 \log^2 (p) /n \to 0$ for any error density having finite variance and a bounded first derivative. No further conditions are imposed on the sequence of design matrices. The result is extended to more general estimates with the property that the average error and average squared error in the fitted values are on the same order as for least squares.
- Published
- 2001
74. Acknowledgement and Announcement
- Author
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Tsung, Fugee, primary, Castagliola, Philippe, additional, and Gemai, Chen, additional
- Published
- 2010
- Full Text
- View/download PDF
75. Independence andtDistribution
- Author
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Gemai Chen and A. Adatia
- Subjects
Statistics and Probability ,General Mathematics ,Statistics ,food and beverages ,Independence (mathematical logic) ,T distribution ,Statistics, Probability and Uncertainty ,Standard normal table ,Mathematical economics ,Random variable ,Mathematics - Abstract
The importance of the independence between a standard normal and a chi-square random variable in constructing a t random variable is explored. When independence is absent it is demonstrated that the usual t approximation can lead to misleading results.
- Published
- 1997
76. Independence and t Distribution
- Author
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Gemai Chen and A. Adatia
- Subjects
Statistics and Probability ,General Mathematics ,Statistics, Probability and Uncertainty - Published
- 1997
77. Weighted profile least squares estimation for a panel data varying-coefficient partially linear model.
- Author
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Bin ZHOU, Jinhong YOU, Qinfeng XU, and Gemai CHEN
- Subjects
LEAST squares ,LINEAR statistical models ,MATHEMATICAL models ,ESTIMATION theory ,STATISTICAL bootstrapping ,POLYNOMIALS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
78. An asymptotic theory for semiparametric generalized least squares estimation in partially linear regression models.
- Author
-
Gemai Chen and Jinhong You
- Subjects
LEAST squares ,ESTIMATION theory ,REGRESSION analysis ,HETEROSCEDASTICITY ,MATHEMATICAL statistics - Abstract
Consider a partially linear regression model with an unknown vector parameter Β, an unknown function g(·), 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. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
79. Millennial-scale relationships of diatom species richness and production in two prairie lakes.
- Author
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Rusak, James A., Leavitt, Peter R., McGowan, Suzanne, Gemai Chen, Olson, Olaf, Wunsam, Sybille, and Cumming, Brian F.
- Subjects
BIODIVERSITY ,SPECIES ,BIOTIC communities ,LAKES ,DIATOMS - 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 (r² = 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 (r² = 0.13-0.45, p < 0.001) and could be eliminated (r² < 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 (r² = 0.09-0.24, p < 0.0001) between past diatom species richness and ratios of stable isotopes (primarily δ
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. [ABSTRACT FROM AUTHOR]- Published
- 2004
- Full Text
- View/download PDF
80. Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity.
- Author
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Jin-hong You and Gemai Chen
- Subjects
REGRESSION analysis ,ANALYSIS of covariance - Abstract
Consider a partially linear regression model with an unknown vector parameter ß, an unknown function g(·), and unknown heteroscedastic error variances. Chen, You
[23] proposed a semiparametric generalized least squares estimator (SGLSE) for ß, 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]. [ABSTRACT FROM AUTHOR]- Published
- 2003
81. Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors.
- Author
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Jin-hong You, Gemai Chen, Min Chen, and Xue-lei Jiang
- Subjects
REGRESSION analysis ,MATHEMATICAL analysis ,MATHEMATICAL statistics - Abstract
Consider the partly linear regression model % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WG5bWaaSbaaSqaaiaadMgaaeqaaOGaeyypa0JabmiEayaafaWaaSba % aSqaaiaadMgaaeqaaOGaeqOSdiMaey4kaSIaam4zamaabmaabaGaam % iDamaaBaaaleaacaWGPbaabeaaaOGaayjkaiaawMcaaiabgUcaRiab % ew7aLnaaBaaaleaacaWGPbaabeaakiaacYcacaaMe8UaaGjbVlaayI % W7caaIXaGaeyizImQaamyAaiabgsMiJkaad6gaaaa!53DA! $$ y_{i} = {x}''_{i} \beta + g{\left( {t_{i} } \right)} + \varepsilon _{i} ,\;\;{\kern 1pt} 1 \leqslant i \leqslant n $$ , where y
i ?s are responses, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WG4bWaaSbaaSqaaiaadMgaaeqaaOGaeyypa0ZaaeWaaeaacaWG4bWa % aSbaaSqaaiaadMgacaaIXaaabeaakiaacYcacaWG4bWaaSbaaSqaai % aadMgacaaIYaaabeaakiaacYcacqWIVlctcaGGSaGaamiEamaaBaaa % leaacaWGPbGaamiCaaqabaaakiaawIcacaGLPaaadaahaaWcbeqaaO % Gamai4gkdiIcaacaaMe8UaaGjbVlaaysW7caqGHbGaaeOBaiaabsga % caaMe8UaaGjbVlaaysW7caWG0bWaaSbaaSqaaiaadMgaaeqaaOGaey % icI4Saamivaaaa!5D82! $$ x_{i} = {\left( {x_{{i1}} ,x_{{i2}} , \cdots ,x_{{ip}} } \right)}^{\prime } \;\;\;{\text{and}}\;\;\;t_{i} \in {\cal T} $$ are known and nonrandom design points, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WGubaaaa!393B! $$ {\cal T} $$ is a compact set in the real line % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WGsbaaaa!3939! $$ {\cal R} $$ , ß = ( ß1 , ··· , ßp )? is an unknown parameter vector, g(·) is an unknown function and { ei } is a linear process, i.e., % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacq % aH1oqzdaWgaaWcbaGaamyAaaqabaGccaaMi8Uaeyypa0JaaGjcVpaa % qahabaGaeqiYdK3aaSbaaSqaaiaadQgaaeqaaOGaamyzamaaBaaale % aacaWGPbGaeyOeI0IaamOAaaqabaGccaGGSaGaaGjcVlaaysW7cqaH % ipqEdaWgaaWcbaGaaGimaaqabaGccaaMi8Uaeyypa0JaaGjcVlaaig % dacaGGSaGaaGjbVlaayIW7daaeWbqaamaaemaabaGaeqiYdK3aaSba % aSqaaiaadQgaaeqaaaGccaGLhWUaayjcSdGaeyipaWJaeyOhIukale % aacaWGQbGaeyypa0JaaGimaaqaaiabg6HiLcqdcqGHris5aaWcbaGa % amOAaiabg2da9iaaicdaaeaacqGHEisPa0GaeyyeIuoaaaa!6ABD! $$ \varepsilon _{i} {\kern 1pt} = {\kern 1pt} {\sum\limits_{j = 0}^\infty {\psi _{j} e_{{i - j}} ,{\kern 1pt} \;\psi _{0} {\kern 1pt} = {\kern 1pt} 1,\;{\kern 1pt} {\sum\limits_{j = 0}^\infty {{\left| {\psi _{j} } \right|} < \infty } }} } $$ , where ej are i.i.d. random variables with zero mean and variance % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacq % aHdpWCdaqhaaWcbaGaamyzaaqaaiaaikdaaaaaaa!3BF8! $$ \sigma ^{2}_{e} $$ . Drawing upon B-spline estimation of g(·) and least squares estimation of ß, we construct estimators of the autocovariances of { ei }. 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 { ei } 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. [ABSTRACT FROM AUTHOR]- Published
- 2003
82. An improved p chart through simple adjustments.
- Author
-
Gemai Chen
- Subjects
FRACTIONS - Abstract
Proposes a chart for an improved monitoring of the p fraction. Two alternatives to the p chart; Guidelines for choosing an appropriate chart; Advantages of simple adjustments; Explanation of T.P. Ryan's rule of thumb.
- Published
- 1998
- Full Text
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83. Jackknifing in partially linear regression models with serially correlated errors
- Author
-
Xian Zhou, Jinhong You, and Gemai Chen
- Subjects
Statistics and Probability ,Jackknife-type estimation ,Numerical Analysis ,Statistics::Theory ,Mean squared error ,Semiparametric least-squares estimator ,Coverage probability ,Estimator ,Serially correlated errors ,Delta method ,Minimum-variance unbiased estimator ,Efficient estimator ,Consistent estimator ,Statistics ,Partially linear regression model ,Statistics::Methodology ,Asymptotic normality ,Consistency ,Statistics, Probability and Uncertainty ,Robustness ,Jackknife resampling ,Mathematics - Abstract
In this paper jackknifing technique is examined for functions of the parametric component in a partially linear regression model with serially correlated errors. By deleting partial residuals a jackknife-type estimator is proposed. It is shown that the jackknife-type estimator and the usual semiparametric least-squares estimator (SLSE) are asymptotically equivalent. However, simulation shows that the former has smaller biases than the latter when the sample size is small or moderate. Moreover, since the errors are correlated, both the Tukey type and the delta type jackknife asymptotic variance estimators are not consistent. By introducing cross-product terms, a consistent estimator of the jackknife asymptotic variance is constructed and shown to be robust against heterogeneity of the error variances. In addition, simulation results show that confidence interval estimation based on the proposed jackknife estimator has better coverage probability than that based on the SLSE, even though the latter uses the information of the error structure, while the former does not.
- Full Text
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84. Convergence rates of estimators in partial linear regression models with MA(∞) error process
- Author
-
Xian Zhou, Gemai Chen, Jinhong You, and Xiaoqian Sun
- Subjects
Statistics and Probability ,Autocovariance ,Rate of convergence ,Statistics ,Linear regression ,Autocorrelation ,Estimator ,Applied mathematics ,Principal component regression ,Law of the iterated logarithm ,Least squares ,Mathematics - Abstract
This paper is concerned with a partial linear regression model with serially correlated random errors which are unobservable and modeled by a moving-average process of infinite order. We study a class of estimators for the linear regression coefficients as well as the function characterizing the non-linear part of the model, constructed based on general kernel smoothing and least squares methods. The law of iterated logarithm and strong convergence rates of these estimator are derived by truncating the moving-average error process, a procedure widely applied in the analysis of time series. Our results can be used to establish uniform strong convergence rate of the estimators of autocovariance and autocorrelation functions of the error process.
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