OPTIMAL　GLOBAL　RATES　OF　CONVERGENCE　OF　M－ESTIMATES　FOR　MULTIVARIATE　NONPARAMETRIC　REGRESSION  

作　　者：施沛德 王学仁 

出　　处：《Acta Mathematicae Applicatae Sinica》1995年第2期139-151,共13页应用数学学报（英文版）

摘　　要：Consider the nonparametric regression model Y=go(T)+u, where Y is real-valued, u is a random error, T is a random d-vector of explanatory variables ranging over a nondegenerate d-dimensional compact set C, and go(·) is the unknown smooth regression function, which is m (0) times continuously differentiable and its mth partial derivatives satisfy the Hǒlder condition with exponent γ∈(0,1], where i1, . . . , id are nonnegative integers satisfying ik=m. The piecewise polynomial estimator of go based on M-estimates is considered. It is proved that the rate of convergence of the underlying estimator is Op () under certain regular conditions, which is the optimal global rate of convergence of least square estimates for nonparametric regression studied in [10-11] .Consider the nonparametric regression model Y=go(T)+u, where Y is real-valued, u is a random error, T is a random d-vector of explanatory variables ranging over a nondegenerate d-dimensional compact set C, and go(·) is the unknown smooth regression function, which is m (0) times continuously differentiable and its mth partial derivatives satisfy the Hǒlder condition with exponent γ∈(0,1], where i1, . . . , id are nonnegative integers satisfying ik=m. The piecewise polynomial estimator of go based on M-estimates is considered. It is proved that the rate of convergence of the underlying estimator is Op () under certain regular conditions, which is the optimal global rate of convergence of least square estimates for nonparametric regression studied in [10-11] .

关 键 词：Nonparametric regression global rate of convergence piecewise polynomial Mestimates 

分 类 号：O212[理学—概率论与数理统计]