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We propose a consistent and locally efficient estimator to estimate the model parameters for a logistic mixed effect model with random slopes. Our approach relaxes two typical assumptions: the random effects being normally distributed, and the covariates and random effects being independent of each other. Adhering to these assumptions is particularly difficult in health studies where in many cases we have limited resources to design experiments and gather data in long-term studies, while new findings from other fields might emerge, suggesting the violation of such assumptions. So it is crucial if we could have an estimator robust to such violations and then we could make better use of current data harvested using various valuable resources. Our method generalizes the framework presented in Garcia & Ma (2016) which also deals with a logistic mixed effect model but only considers a random intercept. A simulation study reveals that our proposed estimator remains consistent even when the independence and normality assumptions are violated. This contrasts from the traditional maximum likelihood estimator which is likely to be inconsistent when there is dependence between the covariates and random effects. Application of this work to a Huntington disease study reveals that disease diagnosis can be further improved using assessments of cognitive performance.

In 2003, Liu proposed a new estimator dealing with the problem of multicollinearity in linear regression model pointing out a drawback of ridge estimator used in this context. This new estimator, called Liu-type estimator was demonstrated to have lesser mean squared error than ridge estimator and ordinary least squares estimator, however, it may carry a large amount of bias. In the present paper, we propose different estimators in order to reduce the bias of Liu-type estimator, one using the Jackknife technique and other using the technique proposed in Kadiyala \cite{kad1984}. We also investigate the Bootstrap method of bias correction on the Liu-type estimator as well. The bias and mean squared error of these estimators have been compared using a simulation study as well as a numerical example. LSTA-2016-0059

Based on the Girsanov theorem, this paper obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and tri-modal, indicating that the estimator is biased. These two properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in the discrete time model, suggesting the classical long-span asymptotic theory is inadequate. The paper then builds a continuous time approximation to the discrete time model and develops an in-fill asymptotic theory for the LS estimator. The in-fill asymptotic distribution is asymmetric and tri-modal and delivers good approximations to the finite sample distribution. To reduce the bias in the estimation of both the continuous time and the discrete time models, a simulation-based method based on the indirect estimation (IE) approach is proposed. Monte Carlo studies show that IE achieves substantial bias reductions.

We propose a kernel estimator for the spot volatility of a semi-martingale at a given time point by using high frequency data, where the underlying process accommodates a jump part of infinite variation. The estimator is based on the representation of the characteristic function of Levy processes. The consistency of the proposed estimator is established under some mild assumptions. By assuming that the jump part of the underlying process behaves like a symmetric stable Levy process around 0, we establish the asymptotic normality of the proposed estimator. In particular, with a specific kernel function, the estimator is variance efficient. We conduct Monte Carlo simulation studies to assess our theoretical results and compare our estimator with existing ones.

This paper compares three types of standard errors for optimal minimum distance (OMD) estimator where the structural parameter is recovered from the reduced form parameters estimated by a two-step GMM estimator. We demonstrate that the naive standard errors are severely biased and cause over-rejection, while the OMD estimator based on the bias-corrected variance matrix by Windmeijer (2005) and newly derived variance estimator yield much more accurate inference.

This paper studies the nonparametric estimator of the quantile function under length-biased and right censored data, with the property of length-bias that the residual lifetime share the same distribution as the truncation time. A nonparametric estimator of the quantile function is proposed based on the improved product-limit estimator of distribution function that takes into account the auxiliary information about the length-biased sampling. Asymptotic properties of the estimator are derived, and numerical simulation studies are conducted to assess the performance of the proposed estimator, an application is also given using the Channing house data.

Regression models for correlated binary outcomes are commonly fit using a Generalized Estimating Equations (GEE) methodology. GEE uses the Liang and Zeger sandwich estimator to produce unbiased standard error estimators for regression coefficients in large sample settings even when the covariance structure is misspecified. The sandwich estimator performs optimally in balanced designs when the number of participants is large, and there are few repeated measurements. The sandwich estimator is not without drawbacks; its asymptotic properties do not hold in small sample settings. In these situations, the sandwich estimator is biased downwards, underestimating the variances. In this project, a modified form for the sandwich estimator is proposed to correct this deficiency. The performance of this new sandwich estimator is compared to the traditional Liang and Zeger estimator as well as alternative forms proposed by Morel, Pan and Mancl and DeRouen. The performance of each estimator was assessed with 95% coverage probabilities for the regression coefficient estimators using simulated data under various combinations of sample sizes and outcome prevalence values with an Independence (IND), Autoregressive (AR) and Compound Symmetry (CS) correlation structure. This research is motivated by investigations involving rare-event outcomes in aviation data.

The least-squares regression estimator can be very sensitive in the presence of multicollinearity and outliers in the data. We introduce a new robust estimator based on the MM estimator. By conside...

We investigate the probabilities of large deviations of the maximum likelihood estimator and Bayes estimator of the drift parameter for a mixed fractional Ornstein-Uhlenbeck type process.

We introduce a robust estimator of the location parameter for the change-point in the mean based on Wilcoxon statistic and establish its consistency for L1 near-epoch dependent processes. It is shown that the consistency rate depends on the magnitude of the change. A simulation study is performed to evaluate the finite sample properties of the Wilcoxon-type estimator under Gaussianity as well as under heavy-tailed distributions and disturbances by outliers, and to compare it with a CUSUM-type estimator. It shows that the Wilcoxon-type estimator is equivalent to the CUSUM-type estimator under Gaussianity but outperforms it in the presence of heavy tails or outliers in the data.

In this paper, we proposed an alternative stochastic restricted Liu-type estimator β^SRLTE for the vector of parameters in a linear regression model. The new estimator is a combination of ordinary mixed estimator β^OME and Liu-Type estimator β^LTE, which was proposed by Liu. Necessary and sufficient conditions for the superiority of new stochastic restricted Liu-type estimator β^SRLTE over the ordinary mixed estimator β^OME and the Liu-type estimator β^LTE in the mean squared error matrix sense are derived for the two cases in which the parametric restrictions are correct and are not correct. In particular, we showed that β^SRLTE was superior in the mean squared error matrix sense over both β^OME and to the Liu-type estimator introduced by Liu (2003).

This paper discusses the parameter estimation in a partially linear model. We proposed a difference-based Liu-type estimator of the unknown parameters in the partially linear model. The asymptotically properties of the proposed estimator are discussed. We propose a iterative method to choose the biasing parameters. Finally, a simulation study and a numerical example are presented to explain the performance of the estimators.

A new estimator for estimating the proportion of a potentially sensitive attribute in survey sampling has been introduced by solving a linear equation. The proposed estimator has been compared with the estimator proposed by Odumade and Singh (2009) with equal protection to all of the respondents. The asymptotic properties of the proposed estimator are investigated through exact numerical illustrations for different choices of parameters. A non randomized response approach has been suggested. A scope for further research has also been pointed out.

This study proposes a more efficient calibration estimator for estimating population mean in stratified double sampling using new calibration weights. The variance of the proposed calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator (CAOE) and its approximate variance estimator are derived for the proposed calibration estimator and existing calibration estimators in stratified double sampling. Analytical results showed that the proposed calibration estimator is more efficient than existing members of its class in stratified double sampling. Analysis and evaluation are presented.

In this paper, we are proposing a modified jackknife Liu-type estimator (MJLTE) that was created by combining the ideas underlying both the Liu-type estimator (LTE) and the jackknifed Liu-t...

This article proposes an alternative to usual ratio estimator of population mean in post-stratified sampling procedure and its properties are analyzed. Both theoretical and empirical findings are encouraging and support the soundness of the proposed procedure for mean estimation over an alternative to ratio estimator in simple random sampling without replacement suggested by Srivenkataramana and Tracy (1980), usual combined ratio estimators suggested by Ige and Tripathi (1989), and usual unbiased estimator in post-stratified sampling scheme. Both theoretical and empirical findings are encouraging and support the soundness of the present study. At the end, a simulation study has been carried out to verify the superiority of the proposed estimator.

This paper considers the problem of estimating the population variance S2y of the study variable y using the auxiliary information in sample surveys. We have suggested the (i) chain ratio-type estimator (on the lines of Kadilar and Cingi (2003)), (ii) chain ratio-ratio-type exponential estimator and their generalized version [on the lines of Singh and Pal (2015)] and studied their properties under large sample approximation. Conditions are obtained under which the proposed estimators are more efficient than usual unbiased estimator s2y and Isaki (1893) ratio estimator. Improved version of the suggested class of estimators is also given along with its properties. An empirical study is carried out in support of the present study.

In this paper, we introduce mixed Liu estimator (MLE) for the vector of parameters in linear measurement error models by unifying the sample and the prior information. The MLE is a generalization o...

In this paper, the preliminary test approach to the estimation of the linear regression model with student's t errors is considered. The preliminary test almost unbiased two-parameter estimator is proposed, when it is suspected that the regression parameter may be restricted to a constraint. The quadratic biases and quadratic risks of the proposed estimators are derived and compared under both null and alternative hypotheses. The conditions of superiority of the proposed estimators for departure parameter and biasing parameters k and d are derived, respectively. Furthermore, a real data example and a Monte Carlo simulation study are provided to illustrate some of the theoretical results.

A generalized estimator is introduced for finite population mean in stratified random sampling when observations are contaminated with measurement errors. Many special cases of the proposed estimator are possible. The bias and mean square error of the proposed family of estimators are derived. The performance of the proposed estimator is evaluated both theoretically and empirically in the presence and absence of measurement error.

In this paper, we propose a new efficient estimator namely Optimal Generalized Logistic Estimator (OGLE) for estimating the parameter in a logistic regression model when there exists multicollinearity among explanatory variables. Asymptotic properties of the proposed estimator are also derived. The performance of the proposed estimator over the other existing estimators in respect of Scalar Mean Square Error criterion is examined by conducting a Monte Carlo simulation.

In this paper we propose a new difference-type estimator in estimating the finite population mean in stratified double sampling by using the ranks of two auxiliary variables as an additional information. The proposed estimator performs better than the usual sample mean estimator, ratio estimator, exponential estimator, Choudhury and Singh (2012) estimator, Vishwakarma and Gangele (2014) estimator, Singh and Khalid (2015) estimator, Khan and Al-Hossain (2016) estimator, Khan (2016) estimator and usual difference estimator. Two real data sets are used to observe the performances of estimators.

This article considers some different parameter estimation methods in logistic regression model. In order to overcome multicollinearity, the almost unbiased ridge-type principal component estimator...

The multivariate Bayesian hierarchical model with independent means has been studied extensively and is widely used in practice. In contrast, the case of dependent means has received scant attention, even though multivariate observations are often correlated. In this paper, we investigate a multivariate heteroscedastic Bayesian hierarchical model in which an informative prior with equicorrelated means is assumed. We estimate the mean vector by the shrinkage estimator based on Stein’s unbiased risk estimation (SURE). It is shown that the squared error loss of the SURE estimator is close to that of an oracle estimator as the number of means grows. Our SURE estimator includes the SURE estimator under independence considered by Xie et al. (2012) as a special case. The finite-sample performance of our estimator is explored via simulations and two real data sets are used for illustration purposes.

In estimating the parameters of the two-parameter Pareto distribution it is well known that the performance of the maximum likelihood estimator deteriorates when sample sizes are small or the underlying model is contaminated. In this paper we propose a new parameter estimator that utilizes a pivotal quantity based on the regression framework, allowing separate estimation of the two parameters in a straightforward manner. The consistency of the estimator is also established. Simulation studies show that the proposed estimator is a competitive, well-rounded robust estimator for both Pareto and contaminated Pareto datasets when the sample sizes are small.

We consider efficient estimation of panel data models with interactive effects, which relies on a high-dimensional inverse covariance matrix estimator. By using a consistent estimator of the error covariance matrix, we can take into account both cross-sectional correlations and heteroskedasticity. In the presence of cross-sectional correlations, the proposed estimator eliminates the cross-sectional correlation bias, and is more efficient than the existing methods. The rate of convergence is also improved. In addition, we find that when the statistical inference involves estimating a high-dimensional inverse covariance matrix, the minimax convergence rate on large covariance estimations is not sufficient for inferences. To address this issue, a new “doubly weighted convergence” result is developed. The proposed method is applied to the US divorce rate data. We find that our more efficient estimator identifies the significant effects of divorce-law reforms on the divorce rate, and provides tighter confidence intervals than existing methods. This provides a confirmation for the empirical findings of Wolfers (2006) under more general unobserved heterogeneity.

In this study an improved version of ratio type exponential estimator is been proposed for estimating average of study variable when the population parameter(s) information of second auxiliary variable is available. The proposed estimator compared with usual unbiased estimator and conventional ratio estimators numerically and hypothetically. The mean square error is also obtained and checked the efficiency of the proposed estimator with usual ratio, Singh and Vishwakarma (2007), Singh et al. (2008), Noor-ul-Amin and Hanif (2012), Yadav et al. (2013) and Sanaullah et al. (2015) estimators.

Survival data collected from a prevalent cohort are subject to left truncation and the analysis is challenging. Conditional approaches for left-truncated data could be inefficient as they ignore the information in the marginal likelihood of the truncation times. Length-biased sampling methods may improve the estimation efficiency but only when the underlying truncation time is uniform; otherwise, they may generate biased estimates. We propose a semiparametric method for left-truncated data under the Cox model with no parametric distributional assumption about the truncation times. Our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood, which eliminates the truncation distribution, yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood. An iterative algorithm is provided to solve for the regression coefficients and the baseline hazard function simultaneously. By empirical process and U-process theories, it has been shown that the proposed estimator is consistent and asymptotically normal with a closed-form consistent variance estimator. Simulation studies show substantial efficiency gain of our estimator in both the regression coefficients and the cumulative baseline hazard function over the conditional approach estimator. When the uniform truncation assumption holds, our estimator enjoys smaller biases and efficiency comparable to that of the full maximum likelihood estimator. An application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method.

In the linear regression model with elliptical errors, a shrinkage ridge estimator is proposed. In this regard, the restricted ridge regression estimator under sub-space restriction is improved by incorporating a general function which satisfies Taylor’s series expansion. Approximate quadratic risk function of the proposed shrinkage ridge estimator is evaluated in the elliptical regression model. A Monte Carlo simulation study and analysis based on a real data example are considered for performance analysis. It is evident from the numerical results that the shrinkage ridge estimator performs better than both unrestricted and restricted estimators in the multivariate t-regression model, for some specific cases.

This paper proposes a pairwise likelihood estimator based on an analytic approximation method for the random effects probit model. It is widely known that the standard approach for the random effects probit model relies on numerical integration and that its likelihood function does not have a closed form. When the number of time periods or the serial correlation across periods is large, the resulting estimator is likely to become biased. This study derives an analytic approximation for the likelihood function of one pair of time periods without relying on typical numerical-integral procedures. We then apply this formula in a pairwise likelihood estimation procedure to derive our estimator, which is obtained as the product of the analytic approximation of the likelihood function for all possible pairs of time periods. A simulation study is conducted for the comparison of our proposed estimator with the estimators for the pooled probit model and Gaussian quadrature procedure. The evidence shows that our proposed estimator enjoys desirable asymptotic properties. In addition, compared to the estimator based on the Gaussian quadrature procedure, our proposed estimator exhibits comparable performances in all the configurations considered in the simulation study and shows superiority for the cases of a large number of time periods and high serial correlation across periods. We apply our proposed estimator to British Household Panel Survey data so as to characterize the trend of working probabilities.

In this paper, we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator (AULE) and ridge estimator (RE) in a linear regression model when multicollinearity presents among the independent variables. Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator, RE, AULE and Liu estimator (LE) in the mean squared error matrix sense are derived, and the optimal biasing parameters are obtained. To illustrate the theoretical findings, a Monte Carlo simulation study is carried out and a numerical example is used.

In a variety of statistical problems, estimation of the conditional distribution function remains a challenge. To this end, a two-stage Bernstein estimator for conditional distribution functions is introduced. The method consists in smoothing a first-stage NadarayaWatson or local linear estimator by constructing its Bernstein polynomial. Some asymptotic properties of the proposed estimator are derived, such as its asymptotic bias, variance and mean squared error. The asymptotic normality of the estimator is also established under appropriate conditions of regularity. Lastly, the performance of the proposed estimator is briefly studied through a few examples.

In this article, we consider the estimation of a partially linear model when stochastic linear restrictions on the parameter components are assumed to hold. Based on the weighted mixed estimator, profile least-squares method, and ridge method, a weighted stochastic restricted ridge estimator of the parametric component is introduced. The properties of the new estimator are also discussed. Finally, a simulation study is given to show the performance of the new estimator.

This article proposes a class of estimators for estimating the population mean of the study variate and analyzes its properties in post-stratified sampling. A computational study is carried out in order to judge the merits of the suggested estimator over conventional simple mean estimator, usual unbiased estimator in post-stratified sampling and other estimators of this category.

As known, the ordinary least-squares estimator (OLSE) is unbiased and also, has the minimum variance among all the linear unbiased estimators. However, under multicollinearity the estimator is generally unstable and poor in the sense that variance of the regression coefficients may be inflated and absolute values of the estimates may be too large. There are several classes of biased estimators in statistical literature to decrease the effect of multicollinearity in the design matrix. Here, based on the Cholesky decomposition, we propose such an estimator which makes the data to be slightly distorted. The exact risk expressions as well as the biases are derived for the proposed estimator. Also, some results demonstrating superiority of the suggested estimator over OLSE are obtained. Finally, a Monte-Carlo simulation study and a real data application related to acetylene data are presented to support our theoretical discussions.

This paper analyses the large sample behaviour of a varying kernel density estimator of the marginal density of a non-negative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator. We also derive an almost sure uniform consistency rate over bounded intervals of this estimator. A finite sample simulation shows some superiority of the proposed density estimator over the one based on a symmetric kernel.

A plug-in estimator is proposed for a local measure of variance explained by regression, termed correlation curve in Doksum et al. (J Am Stat Assoc 89:571–582, 1994), consisting of a two-step spline–kernel estimator of the conditional variance function and local quadratic estimator of first derivative of the mean function. The estimator is oracally efficient in the sense that it is as efficient as an infeasible correlation estimator with the variance function known. As a consequence of the oracle efficiency, a smooth simultaneous confidence band (SCB) is constructed around the proposed correlation curve estimator and shown to be asymptotically correct. Simulated examples illustrate the versatility of the proposed oracle SCB which confirms the asymptotic theory. Application to a 1995 British Family Expenditure Survey data has found marginally significant evidence for a local version of Engel’s law, i.e., food budget share and household real income are inversely related (Hamilton in Am Econ Rev 91:619–630, 2001).

This article considers the problem of variance estimation of a U-statistic. Following the proposal of a linearly extrapolated variance estimator in Wang and Chen (2015), we consider a second-order extrapolation technique and devise a variance estimator that is nearly second-order unbiased. Simulation studies confirm that the second-order extrapolated variance estimator has smaller bias than the linearly extrapolated variance estimator and the jackknife variance estimator across a wide selection of distributions. In addition, the proposal also yields a smaller mean squared error than its counterparts. In the end, we discuss the advantages of the proposed variance estimator in regression analysis and model selection.

Modern statistical problems often involve selection of populations (or genes for example) using the observations. After selecting the populations, it is important to estimate the corresponding parameters. These quantities are called the selected parameters. Using traditional estimators, such as maximum likelihood (ML) estimator, which ignores the selection can result in a large bias. It is, however, known that the Bayes estimator that ignores the selection still works well under the assumed prior distribution. But, when the prior distribution used to derive the Bayes estimator is very different from the "true" prior, the Bayes estimator can fail. The paper aims to construct estimators for the selected parameters which are robust to prior distributions. A generalization of the multiple-shrinkage Stein type estimator proposed by George (1986a, 1986b) is proposed and is shown to have a small selection bias for estimating the selected means and have an attractive small expected mean squared error. With respect to these two criteria, the proposed estimator is generally better than ML estimator, Lindley-James-Stein (LJS) estimator and Efron-Tweedie (Efron, 2011) estimator.

In this article we introduce the weighted mixed Liu-type estimator (WMLTE) based on the weighted mixed and Liu-type estimator (LTE) in linear regression model. We will also present necessary and sufficient conditions for superiority of the weighted mixed Liu-type estimator over the weighted mixed estimator (WME) and Liu type estimator (LTE) in terms of mean square error matrix (MSEM) criterion. Finally, a numerical example and a Monte Carlo simulation is also given to show the theoretical results.

We reveal that the minimum Anderson–Darling (MAD) estimator is a variant of the maximum likelihood method. Furthermore, it is shown that the MAD estimator offers excellent opportunities for paramet...

Forest resource assessments utilizing remotely sensed auxiliary data are becoming increasingly important due to their ability to provide precise estimates of forest parameters at low cost. In presenting results from such surveys, it is important to provide not only estimates of the target parameters, but also their confidence intervals, which provide the range of values wherein the true value is located with a certain level of confidence. If such an interval is narrow the point estimates from the survey can be considered very reliable. In estimating the confidence interval the variance of an estimator must first be estimated. Unbiasedness, i.e. that an estimator on average coincides with the true value, is an important property also for variance estimators. Another important property is that the variance estimator itself has low variance, not least in cases when the variance estimates obtained with the estimator may not be strictly positive. One such important case is when two-stage designs are used to first allocate sample clusters in the form of strips from which auxiliary data, such as metrics derived from airborne laser scanning, are obtained; field data are then derived from sample plots beneath each sample strip in a second stage. In this article we compare two variance estimators for such surveys. The first estimator is a standard estimator suggested in reference textbooks on model-assisted sampling. The second estimator is proposed by the authors, and utilizes the auxiliary data to a larger extent. Through Monte Carlo simulation we show that both variance estimators are approximately unbiased, but that the new estimator is more stable (i.e., has lower empirical variance) and provides empirical confidence interval coverage rates that coincide more closely with the nominal coverage rates.

In this article, we introduce the iterative AK composite estimator for the Current Population Survey. This estimator adopts the AK composite estimator as the initial value and further makes good us...

This article deals with the estimation of population mean under simple random sampling using a new form of ratio estimator. The expression for mean square error and bias has been obtained. An efficiency comparison is considered for proposed estimator with the classical ratio, product and exponential ratio estimator. Finally an empirical study is also carried out to judge the performance of proposed estimator.

The estimation problem of a parameter of interest when some model assumptions may be incorrect is considered. The parameter of interest is defined in a model-independent manner and the estimating procedure selects a model with the smallest mean square error (MSE) as estimated by a proposed MSE estimator. This proposed MSE estimator combines both a nonparametric bootstrap and plug-in estimation in its structure. It requires at least one consistent estimator with a quickly disappearing systematic bias ( $$\sqrt n $$ mean convergence). This estimator is not tied up to a single set of model assumptions (e.g., a class of parametric models), and thus it works across various sets of possibly nonnested classes of statistical models. The derived large sample properties constitute theoretical justification of its use and allow the estimation of the probability of how likely this estimator will have the smallest MSE in a pool of candidate estimators. Multiple simulation studies illustrate the performance of the proposed procedure under various scenarios. A real data example highlights its practical use when a single model is selected from several conceptually different statistical modeling techniques (parametric regression, Cox regression, stratified Cox regression, regression on pseudo-values) and other model selection approaches are not applicable.

The estimation of the frequencies of the sum of multiple resolved exponentials in noise is an important problem due to its application in diverse areas from engineering to chemistry. Yet to date, no low cost Fourier-based algorithm has been successful at obtaining unbiased estimates that achieve the CramrRao lower bound (CRLB) over a wide range of signal-to-noise ratios. In this work, we achieve precisely this goal, proposing a fast yet accurate estimator that combines an iterative frequency-domain interpolation step with a leakage subtraction scheme. By analysing the asymptotic performance and the convergence behaviour of the estimator, we show that the estimate of each frequency converges to the asymptotic fixed point. Thus, the estimator is asymptotically unbiased and the variance is extremely close to the CRLB. We verify the theoretical analysis by extensive simulations, and demonstrate that the proposed algorithm is capable of obtaining more accurate estimates than state-of-the-art high resolution methods while requiring significantly less computational effort. HighlightsAn efficient frequency estimator for multiple resolved complex exponentials in noise is proposed.The proposed estimator is Fourier-based with no singular value decomposition or matrix inversion involved.The variance of the estimates obtained by the proposed method is extremely close to the CramrRao bound.Simulation results show that the proposed estimator can outperform state-of-the-art estimation approaches.

The exponentiated Gumbel model has been shown to be useful in climate modeling including global warming problem, flood frequency analysis, offshore modeling, rainfall modeling and wind speed modeling. Here, we consider estimation of the PDF and the CDF of the exponentiated Gumbel distribution. The following esti- mators are considered: uniformly minimum variance unbiased (UMVU) estimator, maximum likelihood (ML) estimator, percentile (PC) estimator, least squares (LS) estimator and weighted least squares (WLS) estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the ML estimator performs better than others.

Fixed effects panel data regression models are useful tools in econometric and microarray analysis. In this paper, we consider statistical inferences under the setting of fixed effects panel data partially linear regression models with heteroscedastic errors. We find that the usual local polynomial estimator of the error variance function based on residuals is inconsistent, and develop a consistent estimator. Applying this consistent estimator of error variance and spline series approximation of the nonparametric component, we further construct a weighted semiparametric least squares dummy variables estimator for the parametric and nonparametric components. Asymptotic normality of the proposed estimator is derived and its asymptotic covariance matrix estimator is provided. The proposed estimator is shown to be asymptotically more efficient than those ignoring heteroscedasticity. Simulation studies are conducted to demonstrate the finite sample performances of the proposed procedure. As an application, a set of economic data is analyzed by the proposed method.