Statistical Inference Theory Of Partitioning Estimate And Its Modified Estimate For Nonparametric Regression Function Under Dependent Sample

Let (X,Y) be a R^d×R¹ valued random vector and (X₁,Y₁), (X₂,Y₂) …(X_n,Y_n) be a random sample drawn from (X,Y). If E|Y| is finite, the regression function of Y given X is defined as m(x) = E(Y|X = x), x∈R^d . How toestimate m(x) from the sample {(X₁,Y₁),1≤i≤ n} has been one of the most significant things in probability and statistics.Professor Paul Algoet and Professor Laszlo Gyorfi (1999) in the U.S.A proposed partitioning estimate for regressionfunction m (x);then the famous statistician Zhao Ling Cheng (2002) in China proposed the modified partitioning estimate for regression function m(x) and proved its strong consistency under i.i.d sample;based on this,Professor Ling Neng Xiang (2004) proved the strong consistency and convergence rate of modified partitioning estimate for regression function under sample that is identically distributed φ-mixing sequence;he (2005) proved the strong consistency ofpartitioning estimate for regression function under sample that is identically distributed