Consistent Residuals Density Estimation in Nonparametric Regression Under m(n)-Dependent Sample
Received:May 26, 1994  
Key Words: residuals, pointwise and uniform consistency, L1-consistent, k-nearest neigh-bor regression, m(n)-dependent sample.  
Fund Project:The Project Supported by National Natural Science Foundation of China.
Author NameAffiliation
Qin Gengsheng Dept. of Math., Sichuan University, Chengdu 610064 
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Abstract:
      Consider the nonparametric regression model Yi=M(Xi)+ei,where M(x) is an unknown real function on B(?R), {(Xi,Yi)} is a m(n)-dependent sample from (X,Y), the residuals{ei}have unknown common density f(x).In this paper, a non-parametric estimate for f(x)is proposed on the basis of the residuals estimates. The estimate is shown to be pointwise and uniformly consistent and L1-consistent.
Citation:
DOI:10.3770/j.issn:1000-341X.1996.04.005
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