Estimation of Linear Regression Models with Missing Observations on Both the Explanatory and Study Variables

Abstract

This paper discusses the estimation of coefficients in a linear regression model when there are some missing observations on an explanatory variable and the study variable individually as well as simultaneously. The first order regression method of imputation is followed and the least squares procedure is applied. Efficiency properties of estimators are then investigated employing the large sample asymptotic theory.

Key Words:

• Correlation-up-date-modelling
• missing at random
• regression

Additional information

Notes on contributors

H. Toutenburg

Helge Toutenburg received the degree of Ph.D. (Dr. rer. nat) from Humboldt University in Berlin in 1969 and the degree D.Sc. (Econ) from University of Dortmund in 1989. He is a full professor in Statistics at University of Munich. He has about 40 monographs and more than 120 publications and is co-author of C. R. Rao. His research interests are linear models, design of experiments, and missing data.

V. K. Srivastava

V. K. Srivastava received his Ph.D. degree from University of Lucknow (India) in 1973 and specialized in Econometrics and Planning from Indian Statistical Institute (India) in 1974. He was a full professor of Statistics when he passed away in 2001. He wrote more than 150 research papers and 3 books coauthored with Professors D.E.A. Giles and B. B. Rao. His research interests include econometrics, linear models, missing data models, simultaneous equation models, seemingly unrelated regression equation models, sampling theory, and statistical inference.

Shalabh

Shalabh received his Ph.D. degree from University of Lucknow (India) in 1996 and completed post-doc from University of Pittsburgh (U.S.A.) under Professor Leon J. Gleser in 2002. He is an Assistant Professor at Indian Institute of Technology, Kanpur (India). He has written about 50 research papers. His research interests include linear regression models, measurement error models, missing data models, panel data models, restricted regression, forecasting techniques, sampling theory, and statistical inference.