Consistent Estimators Of Regression Coefficients Research Articles

Using stochastic prior information in consistent estimation of regression coefficients in replicated measurement error model

A replicated ultrastructural measurement error regression model is considered where both predictor and response variables are observed with error. Availability of some prior information regarding regression coefficients in the form of stochastic linear restrictions is assumed. Using this prior information, three classes of consistent estimators of regression coefficients are proposed. A two-stage procedure is discussed to obtain feasible version of these Stochastically Restricted estimators. The asymptotic properties of the proposed estimators are studied. No distributional assumption is imposed on any random component of the model. Monte Carlo simulations study is performed to assess the effect of sample size, replicates and non-normality on the estimators. The methods are illustrated using real economic data.

Estimation of Regression Coefficients in a Restricted Measurement Error Model Using Instrumental Variables

The use of instrumental variable approach is extended in measurement error models to the case when regression coefficients are subjected to exact linear restrictions. Some consistent estimators of regression coefficients are obtained which satisfy the restrictions also. We do not make any assumption the distribution of measurement errors and they need not to have necessarily a normal distribution. The asymptotic properties of the estimators are studied. A simulation study is simultaneously conducted to investigate the finite sample properties and compare the efficiencies of the proposed estimators.

Restricted estimation in multivariate measurement error regression model

We study a multivariate ultrastructural measurement error (MUME) model with more than one response variable. This model is a synthesis of multivariate functional and structural models. Three consistent estimators of regression coefficients, satisfying the exact linear restrictions have been proposed. Their asymptotic distributions are derived under the assumption of a non-normal measurement error and random error components. A simulation study is carried out to investigate the small sample properties of the estimators. The effect of departure from normality of the measurement errors on the estimators is assessed.

Consistent estimation of regression coefficients in ultrastructural measurement error model using stochastic prior information

The problem of consistent estimation of regression coefficients in a multivariate linear ultrastructural measurement error model is considered in this article when some additional information on regression coefficients is available a priori. Such additional information is expressible in the form of stochastic linear restrictions. Utilizing stochastic restrictions given a priori, some methodologies are presented to obtain the consistent estimators of regression coefficients under two types of additional information separately, viz., covariance matrix of measurement errors and reliability matrix associated with explanatory variables. The measurement errors are assumed to be not necessarily normally distributed. The asymptotic properties of the proposed estimators are derived and analyzed analytically as well as numerically through a Monte Carlo simulation experiment.

Transition Models for Multivariate Longitudinal Binary Data

In many settings with longitudinal binary data, interest lies in modeling covariate effects on transition probabilities of an underlying stochastic process. When data from two or more processes are available, the scientific focus may be on the degree to which changes in one process are associated with changes in another process. Analysis based on independent Markov models permits separate examination of covariate effects on the transition probabilities for each process, but no insight into between-process associations is obtained. We propose a method of estimation and inference based on joint transitional models for multivariate longitudinal binary data using GEE2 or alternating logistic regression that allows modeling of covariate effects on marginal transition probabilities as well as the association parameters. Consistent estimates of regression coefficients and association parameters are obtained, and efficiency gains for the parameters governing the marginal transition probabilities are realized when the association between processes is strong. Extensions to deal with multivariate longitudinal categorical data are indicated.

Improved Estimation in Measurement Error Models Through Stein Rule Procedure

This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares procedure and yields consistent estimators of regression coefficients. A further application may improve the efficiency properties of the estimators of regression coefficients. It is observed that the proposed family of estimators under some constraint on the characterizing scalar dominates the conventional consistent estimator with respect to the criterion of asymptotic risk under a specific quadratic loss function. Then the problem of prediction of the values of the study variable within the sample is considered, and it is found that the predictors based on the proposed family of estimators are always more efficient than the predictors based on the conventional estimator according to asymptotic predictive mean squared error criterion, although both are biased.

Fisher consistency of GEE models under link misspecification

Liang and Zeger (1986) introduced generalized estimating equation or GEE models as a way of using the ideas of generalized linear models when repeated measures are available on subjects or clusters of subjects, but normality of the response may not be appropriate. They have shown that consistent estimates of regression coefficients are obtained even if the within cluster or subject correlation is misspecified. In this article we show that under certain common circumstances, Fisher consistent estimates of regression coefficients will be obtained even if the link function in the generalized linear model is misspecified.

On strongly consistent estimates of regression coefficients when the errors are not independently and identically distributed

In this paper, the author proposes two methods of estimation of the regression coefficients when the errors are not distributed identically and independently and have a nonzero mean. The estimates proved in this paper are shown to be strongly consistent and mean square consistent.

Consistent moment estimators of regression coefficients in the presence of errors in variables

This paper examines the possibilities of moment estimators of regression coefficients in the errors-in-variables problem suggested by Geary (1942) and others [Scott (1950) and Drion (1951)]. This approach yields consistent estimators of regression coefficients based on uni- and bi-variate moments (or cumulants) of third or higher order. These are computationally simple and need milder assumptions than the standard techniques, viz., ML and IV estimation. After a review of past investigations, this paper proposes new moment estimators and compares the asymptotic efficiencies of six estimators proposed earlier or here and of the OLS estimator. The case where the true regressor is lognormally distributed receives considerable attention in this communication.