秦更生.m(n)-相依样本非参数回归残差密度的相合估计(英文)[J].数学研究及应用,1996,16(4):505~516
m(n)-相依样本非参数回归残差密度的相合估计(英文)
Consistent Residuals Density Estimation in Nonparametric Regression Under m(n)-Dependent Sample
投稿时间:1994-05-26  
DOI:10.3770/j.issn:1000-341X.1996.04.005
中文关键词:  
英文关键词:residuals, pointwise and uniform consistency, L1-consistent, k-nearest neigh-bor regression, m(n)-dependent sample.
基金项目:
作者单位
秦更生 四川大学数学系 
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中文摘要:
      考虑非参数回归模型:Yi=M(Xi)+ei,其中M(x)为B(?R)上的未知实函数,(Xi,Yi)为来自(X,Y)的m(n)相依样本,残差(ei)具有公共的未知密度f(x).本文基于残差估计给出了f(x)的一种非参估计,并证明该估计具有逐点相合性,一致相合性及L1相合性.
英文摘要:
      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.
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