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June, 1995 Nonparametric Regression Under Long-Range Dependent Normal Errors
Sandor Csorgo, Jan Mielniczuk
Ann. Statist. 23(3): 1000-1014 (June, 1995). DOI: 10.1214/aos/1176324633


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.


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Sandor Csorgo. Jan Mielniczuk. "Nonparametric Regression Under Long-Range Dependent Normal Errors." Ann. Statist. 23 (3) 1000 - 1014, June, 1995.


Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0852.62035
MathSciNet: MR1345211
Digital Object Identifier: 10.1214/aos/1176324633

Primary: 62G07
Secondary: 60F17 , 62M99

Keywords: finite-dimensional distributions , Fixed design , kernel regression estimators , long-range dependence , maximal deviations

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • June, 1995
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