Unbiased prediction in linear regression models with equi-correlated responses

This paper considers the problem of predicting the actual and mean values of response variable in a linear regression model with equi-correlated responses. Two such predictors are presented and their efficiency properties are studied with respect to the criterion of covariance matrix.     

Estimation of regression models with equi-correlated responses when some observations on the response variable are missing

The present article deals with the problem of estimation of parameters in a linear regression model when some data on response variable is missing and the responses are equi-correlated. The ordinary least squares and optimal homogeneous predictors are employed to find the imputed values of missing observations. Their efficiency properties are analyzed using the small disturbances asymptotic theory. The estimation of regression coefficients using these imputed values is also considered and a comparison of estimators is presented.     

Consistent Estimation of the Regression Coefficient Through Weighted Arithmetic Mean of the Inconsistent Estimators in Replicated Ultrastructural Model

The problem of consistent estimation of the slope parameter in an ultrastructural model with replicated observations is considered in this article. A consistent estimator based on a weighted arithmetic mean of two inconsistent least squares estimators is proposed which is independent of any unknown quantity. The efficiency properties of this estimator are studied.     

CONSISTENT ESTIMATION THROUGH WEIGHTED HARMONIC MEAN OF INCONSISTENT ESTIMATORS IN REPLICATED MEASUREMENT ERROR MODELS

The present paper proposes a consistent estimator of slope parameter in a replicated measurement error model arising from the weighted harmonic average of two estimators which are themselves inconsistent.     

Prediction of values of variables in linear measurement error model

This article presents the framework of a linear measurement error model for analysing the data in environmental studies where observations on variables are subjected to measurement errors. The problem of predicting the average and actual values of such variables separately as well as simultaneously are discussed. The methods of ordinary least squares, joint least squares and generalized least squares are employed to construct the predictors. Efficiency properties of these predictors are derived and their comparative study is made. These predictors are exposed to a data set and their performance properties are analysed.     

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.     

Amputation versus imputation of missing values through ratio method in sample surveys

In this article, we consider the estimation of a population mean when some observations on the study characteristic are missing in the bivariate sample data. In all, five estimators are presented and their efficiency properties are discussed. One estimator arises from the the amputation of incomplete observations while the remaining four estimators are formulated using imputed values obtained by the ratio method of estimation. This work was carried out before Professor V.K. Srivastava passed away in 2001.