Anil K. Srivastava

The coefficient of determination and its adjusted version in linear regression models

This article presents a comparative study of the efficiency properties of the coefficient of determination and its adjusted version in linear regression models when disturbances are not necessarily normal.

Consistent estimation for the non-normal ultrastructural model

The present article considers the linear ultrastructural model which encompasses the two popular forms of measurement error models, viz., the functional and structural models. The measurement error variance associated with the explanatory variable is assumed to be known which leads to consistent estimators of parameters. The efficiency properties of the thus obtained estimators of slope parameter, intercept term and the measurement error variance of study variable are derived under non-normal error distributions and the effects of departures from symmetry and peakedness of the error distributions are studied.

Comparison of operational variants of best homogeneous and heterogeneous estimators in linear regression

Several adaptive versions of the minimum mean squared error estimator of the coefficient vector in a linear regression model are proposed in the literature. Some of these are compared here, and another estimator is also proposed.

Pitman closeness for Stein-rule estimators of regression coefficients

For estimating the coefficients in a linear regression model, the Stein-rule estimators are considered and their performance is studied according to the criterion of Pitman closeness. For this purpose, an asymptotic approximation for the criterion is derived and analyzed.

Improved estimation of the slope parameter in a linear ultrastructural model when measurement errors are not necessarily normal

Abstract An ultrastructural model framework of linear regression relationship between the study and explanatory variables is considered which allows a comprehensive treatment of the classical linear regression model which is free from contamination and the two popular forms, viz., the functional and the structural, of the measurement error model under one roof. Assuming knowledge of the variance of the measurement errors associated with explanatory variable, a consistent class of the slope parameter has been considered and large-sample asymptotic properties have been studied when distributions of measurement errors are not necessarily normal.

A new property of Stein procedure in measurement error model

Stein-rule procedure is a known technique for yielding biased but efficient estimators of parameters. This article demonstrates that it can be utilized for overcoming the inconsistency of least squares estimators in measurement error models and therefrom providing a class of consistent estimators.

A note on moments of k-class estimators for negative k

The validity of expressions for the exact moments of k-class estimator with 0≦1E;k<1 is established for negative values of k in the interval (–1,0). For other negative values (–∞<k≦1E;–1) the derivation of expressions for moments is outlined.

A synthesis of stein-rule and mixed regression procedures inlinear regression models under non-normality

Stein-rule philosophy and mixed regression technique are combined to develop two families of improved estimators of regression coefficients in the linear regression model under incomplete prior information. The properties of these estimators are studied when disturbances are small and non-normal. Conditions for their dominance over mixed regression estimator are derived taking risk as the criterion for performance.

A feasible minimum risk estimator interpretation to Stein-rule estimators in linear regression model

In this note we furnish a set-up under which the Stein-rule estimator turns out to be a feasible version of the minimum risk estimator.

Estimation of linear regression model with rank deficient observations matrix under linear restrictions

The linear regression model with rank deficient observation matrix is postulated and Schmidts estimator for coefficient vector is considered. An alternative to Schmidts estimator is proposed and a natural generalization is suggested which helps in simplification of Schmidts estimator.