NONPARAMETRIC REGRESSION UNDER LONG-RANGE DEPENDENT NORMAL ERRORS
成果类型：
Article
署名作者：
CSORGO, S; MIELNICZUK, J
署名单位：
Polish Academy of Sciences; Institute of Computer Science of the Polish Academy of Sciences
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176324633
发表日期：
1995
页码：
1000-1014
关键词：
摘要：
We consider the fixed-design regression model with long-range dependent normal errors and show that the finite-dimensional distributions of the properly normalized Gasser-Muller and Priestley-Chao estimators of the regression function converge to those of a white noise process. Furthermore, the distributions of the suitably renormalized maximal deviations over an increasingly finer grid converge to the Gumbel distribution. These results contrast with our previous findings for the corresponding problem of estimating the marginal density of long-range dependent stationary sequences.