Estimation of Parameters in Multiple Regression With Missing X-Observations using Modified First Order Regression Procedure

This paper considers the estimation of coefficients in a linear regression model with missing observations in the independent variables and introduces a modification of the standard first order regression method for imputation of missing values. The modification provides stochastic values for imputation. Asymptotic properties of the estimators for the regression coefficients arising from the proposed modification are derived when either both the number of complete observations and the number of missing values grow large or only the number of complete observations grows large and the number of missing observations stays fixed. Using these results, the proposed procedure is compared with two popular procedures - one which utilizes only the complete observations and the other which employs the standard first order regression imputation method for missing values. It is suggested that an elaborate simulation experiment will be helpful to evaluate the gain in efficiency especially in case of discrete regressor variables and to examine some other interesting issues like the impact of varying degree of multicollinearity in explanatory variables. Applications to some concrete data sets may also shed some light on these aspects. Some work on these lines is in progress and will be reported in a future article to follow