Missing Data, Linear Regression Statistical Inference

In this paper ,we develop inference tools in a linear regression model with missing response data.Let X be a d-dimensional vector of factors and let Y be a response variable influenced by X.In practice,one often obtains a random sample of incomplete data (Xi, Yi, δi),where all the Xi's are observed and δi = 0 if Yi is missing and δi = 1 otherwise.Throughout this article,we assume that Y is Missing at random(MAR).The MAR assumption implies that S and Y are conditionally independent given X, That is,P(δ= 1 | Y, X) = P(δ = 1 | X).A class of estimators is defined that includes as special cases a linear regression imputation estimators marginal average estimator,and a propensity score weighted estimator. We show that any of our class of estimators is asymptotically normal.We show that the jackknife method can be used to consistently estimate the asymptotic variance.The empirical likelihood method is developed ,an adjusted empirical log-likelihood ratio,which is asymptotically standard chisquared,is obtained.Based on biases and standard errors, a comparison is made by simulation between the proposed estimators and the related estimators.