基于半参数方法的模型辅助抽样估计研究

在总结现有模型辅助估计方法的基础上,本文通过构造一种半参数超总体模型,同时结合广义差分估计思想提出一种新型的模型辅助估计量。该估计量比传统的非参数和半参数回归估计利用更少、更易得到的辅助信息,即只需利用和广义回归估计相同的辅助信息,但一般会比广义回归估计拥有更高的估计精度。理论证明了该估计量是渐近设计无偏和设计一致的,其渐近设计均方误差为广义差分估计量的方差。模拟结果显示：其至少与广义回归估计一样好;对于线性程度越低的超总体模型,其估计精度比广义回归估计有越明显的提高;就本文模拟而言,光滑参数在0.04～0.12间适当取值时其会取到相对较好的估计效果。     

Multivariate generalized Birnbaum—Saunders kernel density estimators

In this article, we first propose the classical multivariate generalized Birnbaum–Saunders kernel estimator for probability density function estimation in the context of multivariate non negative data. Then, we apply two multiplicative bias correction (MBC) techniques for multivariate kernel density estimator. Some properties (bias, variance, and mean integrated squared error) of the corresponding estimators are also investigated. Finally, the performances of the classical and MBC estimators based on family of generalized Birnbaum–Saunders kernels are illustrated by a simulation study.     

A generalized inverse regression estimator in multi-univariate linear calibration

A multivariate linear calibration problem, in which response variable is multivariate and explanatory variable is univariate, is considered. In this paper a class of generalized inverse regression estimators is proposed in multi-univariate linear calibration. It includes the classical estimator and the inverse regression one (or Krutchkoff estimator). For the proposed estimator we derive the expressions of bias and mean square error (MSE). Furthermore the behavior of these characteristics is investigated through an analytical method. In addition through a numerical study we confirm the existence of a generalized inverse regression estimator to improve both the classical and the inverse regression estimators on the MSE criterion.     

Uniformly best estimation in linear regression when prior information is fuzzy

Modeling prior information as a fuzzy set and using Zadeh’s extension principle, a general approach is presented how to rate linear affine estimators in linear regression. This general approach is applied to fuzzy prior information sets given by ellipsoidal α-cuts. Here, in an important and meaningful subclass, a uniformly best linear affine estimator can be determined explicitly. Surprisingly, such a uniformly best linear affine estimator is optimal with respect to a corresponding relative squared error approach. Two illustrative special cases are discussed, where a generalized least squares estimator on the one hand and a general ridge or Kuks–Olman estimator on the other hand turn out to be uniformly best.     

A generalized quantile estimator

An alternative to the conventional sample quantlle Is proposed as a nonparametrlc estimator of a continuous population quantlle.The alternative estimator Is a "generalized sample quantlle" obtained by averaging an appropriate subsample quantlle over all subsamples of .a fixed size.Since the resulting statistic is a U-statistic with representation also as a linear combination of order statistics, known results are employed then to establish asymptotic normality.The alternative estimator is shown to be asymptotically efficient in the class of nonparametrlc models specified by Pfanzagl (1975).Analytic results and Monte Carlo studies with a moderate sample size for a variety of distributions Indicate that the proposed estimator usually provides mean square error of estimation less than that of the conventional sample quantile.     

Combining poisson means

The problem of estimating the Poisson mean is considered based on the two samples in the presence of uncertain prior information (not in the form of distribution) that two independent random samples taken from two possibly identical Poisson populations. The parameter of interest is λ₁ from population I. Three estimators, i.e. the unrestricted estimator, restricted estimator and preliminary test estimator are proposed. Their asymptotic mean squared errors are derived and compared; parameter regions have been found for which restricted and preliminary test estimators are always asymptotically more efficient than the classical estimator. The relative dominance picture of the estimators is presented. Maximum and minimum asymptotic efficiencies of the estimators relative to the classical estimator are tabulated. A max-min rule for the size of the preliminary test is also discussed. A Monte Carlo study is presented to compare the performance of the estimator with that of Kale and Bancroft (1967).     

Generalized preliminary test stochastic restricted estimator in the linear regression model

ABSTRACT

In this paper, we propose three generalized estimators, namely, generalized unrestricted estimator (GURE), generalized stochastic restricted estimator (GSRE), and generalized preliminary test stochastic restricted estimator (GPTSRE). The GURE can be used to represent the ridge estimator, almost unbiased ridge estimator (AURE), Liu estimator, and almost unbiased Liu estimator. When stochastic restrictions are available in addition to the sample information, the GSRE can be used to represent stochastic mixed ridge estimator, stochastic restricted Liu estimator, stochastic restricted almost unbiased ridge estimator, and stochastic restricted almost unbiased Liu estimator. The GPTSRE can be used to represent the preliminary test estimators based on mixed estimator. Using the GPTSRE, the properties of three other preliminary test estimators, namely preliminary test stochastic mixed ridge estimator, preliminary test stochastic restricted almost unbiased Liu estimator, and preliminary test stochastic restricted almost unbiased ridge estimator can also be discussed. The mean square error matrix criterion is used to obtain the superiority conditions to compare the estimators based on GPTSRE with some biased estimators for the two cases for which the stochastic restrictions are correct, and are not correct. Finally, a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings of the proposed estimators.     

Two-Stage Welsh's Trimmed Mean for the Simultaneous Equations Model

This paper discusses the large sample theory of the two-stage Welsh's trimmed mean for the limited information simultaneous equations model. Besides having asymptotic normality, this trimmed mean, as the two-stage least squares estimator, is a generalized least squares estimator. It also acts as a robust Aitken estimator for the simultaneous equations model. Examples illustrate real data analysis and large sample inferences based on this trimmed mean.     

On the estimation of the mean vector of a multivariate normal distribution under symmetry

The problem of estimation of the mean vector of a multivariate normal distribution with unknown covariance matrix, under uncertain prior information (UPI) that the component mean vectors are equal, is considered. The shrinkage preliminary test maximum likelihood estimator (SPTMLE) for the parameter vector is proposed. The risk and covariance matrix of the proposed estimato are derived and parameter range in which SPTMLE dominates the usual preliminary test maximum likelihood estimator (PTMLE) is investigated. It is shown that the proposed estimator provides a wider range than the usual premilinary test estimator in which it dominates the classical estimator. Further, the SPTMLE has more appropriate size for the preliminary test than the PTMLE.     

GMM Estimation of Count-Panel-Data Models With Fixed Effects and Predetermined Instruments

The “traditional” approach to the estimation of count-panel-data models with fixed effects is the conditional maximum likelihood estimator. The pseudo maximum likelihood principle can be used in these models to obtain orthogonality conditions that generate a robust estimator. This estimator is inconsistent, however, when the instruments are not strictly exogenous. This article proposes a generalized method of moments estimator for count-panel-data models with fixed effects, based on a transformation of the conditional mean specification, that is consistent even when the explanatory variables are predetermined. Two applications are discussed, the relationship between patents and research and development expenditures and the explanation of technology transfer.     

A Robust Variable Selection to t-type Joint Generalized Linear Models via Penalized t-type Pseudo-likelihood

Although the t-type estimator is a kind of M-estimator with scale optimization, it has some advantages over the M-estimator. In this article, we first propose a t-type joint generalized linear model as a robust extension to the classical joint generalized linear models for modeling data containing extreme or outlying observations. Next, we develop a t-type pseudo-likelihood (TPL) approach, which can be viewed as a robust version to the existing pseudo-likelihood (PL) approach. To determine which variables significantly affect the variance of the response variable, we then propose a unified penalized maximum TPL method to simultaneously select significant variables for the mean and dispersion models in t-type joint generalized linear models. Thus, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the mean and dispersion models. With appropriate selection of the tuning parameters, we establish the consistency and the oracle property of the regularized estimators. Simulation studies are conducted to illustrate the proposed methods.     

Quantile Regression for Location‐Scale Time Series Models with Conditional Heteroscedasticity

This paper considers quantile regression for a wide class of time series models including autoregressive and moving average (ARMA) models with asymmetric generalized autoregressive conditional heteroscedasticity errors. The classical mean‐variance models are reinterpreted as conditional location‐scale models so that the quantile regression method can be naturally geared into the considered models. The consistency and asymptotic normality of the quantile regression estimator is established in location‐scale time series models under mild conditions. In the application of this result to ARMA‐generalized autoregressive conditional heteroscedasticity models, more primitive conditions are deduced to obtain the asymptotic properties. For illustration, a simulation study and a real data analysis are provided.     

On generalized least squares estimation of the weibull distribution

A simple estimation procedure, based on the generalized least squares method, for the parameters of the Weibull distribution is described and investigated. Through a simulation study, this estimation technique is compared with maximum likelihood estimation, ordinary least squares estimation, and Menon's estimation procedure; this comparison is based on observed relative efficiencies (that is, the ratio of the Cramer-Rao lower bound to the observed mean squared error). Simulation results are presented for samples of size 25. Among the estimators considered in this simulation study, the generalized least squares estimator was found to be the "best" estimator for the shape parameter and a close competitor to the maximum likelihood estimator of the scale parameter.     

Cox regression analysis in presence of collinearity: an application to assessment of health risks associated with occupational radiation exposure

This paper considers the analysis of time to event data in the presence of collinearity between covariates. In linear and logistic regression models, the ridge regression estimator has been applied as an alternative to the maximum likelihood estimator in the presence of collinearity. The advantage of the ridge regression estimator over the usual maximum likelihood estimator is that the former often has a smaller total mean square error and is thus more precise. In this paper, we generalized this approach for addressing collinearity to the Cox proportional hazards model. Simulation studies were conducted to evaluate the performance of the ridge regression estimator. Our approach was motivated by an occupational radiation study conducted at Oak Ridge National Laboratory to evaluate health risks associated with occupational radiation exposure in which the exposure tends to be correlated with possible confounders such as years of exposure and attained age. We applied the proposed methods to this study to evaluate the association of radiation exposure with all-cause mortality.     

An effective approach to linear calibration estimation with its applications

Abstract

The availability of some extra information, along with the actual variable of interest, may be easily accessible in different practical situations. A sensible use of the additional source may help to improve the properties of statistical techniques. In this study, we focus on the estimators for calibration and intend to propose a setup where we reply only on first two moments instead of modeling the whole distributional shape. We have proposed an estimator for linear calibration problems and investigated it under normal and skewed environments. We have partitioned its mean squared error into intrinsic and estimation components. We have observed that the bias and mean squared error of the proposed estimator are function of four dimensionless quantities. It is to be noticed that both the classical and the inverse estimators become the special cases of the proposed estimator. Moreover, the mean squared error of the proposed estimator and the exact mean squared error of the inverse estimator coincide. We have also observed that the proposed estimator performs quite well for skewed errors as well. The real data applications are also included in the study for practical considerations.     

A New Class of Credibility Estimators Under the Generalized Weighted Premium Principle

The generalized weighted premium includes many classical premium principles. Most important of all, some of them have positive safe-loading. Some work had been done previously, the credibility premium derived under this premium principle cannot be applied to practice directly due to the difficulties of calculation and the estimation of structure parameters. In this article, we consider a new form of credibility estimator under the generalized weighted premium principle. In addition, the consistency of the estimator is shown and the comparisons were analyzed with previous results in the simulations. The results show that this “new” estimator is better than existed estimators under mean square error sense. Finally, the structure parameters in credibility factor were estimated in the models of multitude contracts.     

Estimating the Population Survival Function Using Additional Information Recorded Over Time: a Filter Based Approach

Survival studies often collect information about covariates. If these covariates are believed to contain information about the life-times, they may be considered when estimating the underlying life-time distribution. We propose a non-parametric estimator which uses the recorded information about the covariates. Various forms of incomplete data, e.g. right-censored data, are allowed. The estimator is the conditional mean of the true empirical survival function given the observed history, and it is derived using a general filtering formula. Feng & Kurtz (1994) showed that the estimator is the Kaplan–Meier estimator in the case of right-censoring when using the observed life-times and censoring-times as the observed history. We take the same approach as Feng & Kurtz (1994) but in addition we incorporate the recorded information about the covariates in the observed history. Two models are considered and in both cases the Kaplan–Meier estimator is a special case of the estimator. In a simulation study the estimator is compared with the Kaplan–Meier estimator in small samples.     

Estimation of parameters in a generalized GMANOVA model based on an outer product analogy and least squares

This paper investigates estimation of parameters in a combination of the multivariate linear model and growth curve model, called a generalized GMANOVA model. Making analogy between the outer product of data vectors and covariance yields an approach to directly do least squares to covariance. An outer product least squares estimator of covariance (COPLS estimator) is obtained and its distribution is presented if a normal assumption is imposed on the error matrix. Based on the COPLS estimator, two-stage generalized least squares estimators of the regression coefficients are derived. In addition, asymptotic normalities of these estimators are investigated. Simulation studies have shown that the COPLS estimator and two-stage GLS estimators are alternative competitors with more efficiency in the sense of sample mean, standard deviations and mean of the variance estimates to the existing ML estimator in finite samples. An example of application is also illustrated.     

Estimation of rare and clustered population variance in adaptive cluster sampling

Abstract

Many researchers used auxiliary information together with survey variable to improve the efficiency of population parameters like mean, variance, total and proportion. Ratio and regression estimation are the most commonly used methods that utilized auxiliary information in different ways to get the maximum benefits in the form of high precision of the estimators. Thompson first introduced the concept of Adaptive cluster sampling, which is an appropriate technique for collecting the samples from rare and clustered populations. In this article, a generalized exponential type estimator is proposed and its properties have been studied for the estimation of rare and highly clustered population variance using single auxiliary information. A numerical study is carried out on a real and artificial population to judge the performance of the proposed estimator over the competing estimators. It is shown that the proposed generalized exponential type estimator is more efficient than the adaptive and non adaptive estimators under conventional sampling design.     

A two-step robust estimation of the process mean using M-estimator

Parameter estimation is the first step in constructing control charts. One of these parameters is the process mean. The classical estimators of the process mean are sensitive to the presence of outlying data and subgroups which contaminate the whole data. In existing robust estimators for the process mean, the effects of the presence of the individual outliers are being considered, while, in this paper, a robust estimator is being proposed to reduce the effect of outlying subgroups as well as the individual outliers within a subgroup. The proposed estimator was compared with some classical and robust estimators of the process mean. Although, its relative efficiency is fourth among the estimators tested, its robustness and efficiency are large when the outlying subgroups are present. Evaluation of the results indicated that the proposed estimator is less sensitive to the presence of outliers and the process mean performs well when there are no individual outliers or outlying subgroups.