Expectation Estimator In Missing Data

About missing data,let(X,Y)be a 2-dimensional random variable and let Y be a response variable influenced by X,Xis a co-variable.In practice,we often obtains a random sample of incomplete data(X_i,Y_i,δ_i),where all the X_i are observedδ_i=0 if Y_i is missing andδ_i=1 otherwise.Throughout this article,we assume that Y is missing completely at random(MCAR).The MCAR assumption implies thatδand(X,Y) are independent,that is P(δ₁=1)=P(δ₂=1)=…=P(δ_n=1)=p.In the first chapter,we introduce the background of the problems which we will study.In the chapter 2,we give an estimator of EY,when no identical function between X and Y exsits.In chapter 3,we obtain an estimator through nonparametric regression,and a comparison is made by simulation between the two estimators in chapter 4.