Statistical Inference Theory Of Partitioning Estimation And Its Modified Estimation For Nonparametric Regression Function

Let (X1, Y1), (X2, Y2) ... (Xn, Yn) be random vectors taking values in Rd R1 with E| Y| < . The regression function of Y given X is defined as m(x) = E(Y|X = x), x R . How to estimate m( x) from the samples { (Xi, Y,) } has been one of the most importement things in probability and statistics. There are two mainly estimation methords such as kernal estimation and its modified kernal estimation, nearest estimation and its modified nearest estimation in literature, whose large sample properties had been researched under i i d samples and some dependence samples such as - mixing.Recently, Professor Paul Algoet and Professor Luszlo Gyorfi(1999) in the U S A proposed partitioning estimation for regression function; then the famous statistician Zhao Ling Chen (2002) in China also proposed the modified partitioning estimation for regression function m( x) and proved its strong consistency under i i d samples, By research, we know that there are many..other large samples properties such as asymptolic normaity, strong consistence for censored data and dependence sumples, etc, which haven't been reseached for years. On the other hand, they play an important role in the theories of esfimation for regression function.In this paper, we mainly get the large sample properties for partitioning estiona-tion and modified its estimation. For example, we proved their asymptolic normaity under nuture conditions by means of mortingle theory; we also get their strong consistency for regression function under censored samples; and finaly we genearzed the result to dependence sample and have strong consistency for the modified partitioning estimation of regression function.