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.