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M-Estimation in the partially linear model with Bernstein polynomials under shape constrains
Authors:Jianhua Ding
Affiliation:1. College of Applied Sciences, Beijing University of Technology, Beijing, P. R. China;2. Department of Mathematics, Shanxi Datong University, Shanxi, P. R. China
Abstract:We develope an M-estimator for partially linear models in which the nonparametric component is subject to various shape constraints. Bernstein polynomials are used to approximate the unknown nonparametric function, and shape constraints are imposed on the coefficients. Asymptotic normality of regression parameters and the optimal rate of convergence of the shape-restricted nonparametric function estimator are established under very mild conditions. Some simulation studies and a real data analysis are conducted to evaluate the finite sample performance of the proposed method.
Keywords:Bernstein polynomials  Empirical process  M-estimation  Rate of convergence  Shape constrains
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