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

This paper considers the estimation of coe cients in a linear regression model with missing observations in the independent variables and intro duces a modi cation of the standard rst order regression method for imputation of missing values The modi cation provides stochastic values for imputation Asymptotic properties of the estimators for the regression coe cients arising from the proposed modi cation are derived when ei ther 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 xed 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 rst order regression imputation method for missing values It is suggested that an elaborate simulation experiment will be helpful to evaluate the gain in e ciency 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