Missing Observations in Multivariate Statistics III: Large Sample Analysis of Simple Linear Regression
Abstract We derive the asymptotic distribution of several estimators for the parameters of the linear regression of y on x when some observations on y and on x are missing. Then, we compare estimators using a mean square error criterion. We find for example that a simple estimator of the linear regression function has asymptotic efficiency no worse than 0.95 compared with the maximum likelihood estimator (assuming bivariate normality) provided that no more than 30 per cent of the y's and 30 per cent of the x's are missing. This simple estimator is defined without assuming bivariate normality in Section 8.1.