The Annals of Statistics

Nonparametric Regression Under Long-Range Dependent Normal Errors

Sandor Csorgo and Jan Mielniczuk

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 23, Number 3 (1995), 1000-1014.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324633

Digital Object Identifier
doi:10.1214/aos/1176324633

Mathematical Reviews number (MathSciNet)
MR1345211

Zentralblatt MATH identifier
0852.62035

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62M99: None of the above, but in this section 60F17: Functional limit theorems; invariance principles

Keywords
Long-range dependence kernel regression estimators fixed design maximal deviations finite-dimensional distributions

Citation

Csorgo, Sandor; Mielniczuk, Jan. Nonparametric Regression Under Long-Range Dependent Normal Errors. Ann. Statist. 23 (1995), no. 3, 1000--1014. doi:10.1214/aos/1176324633. https://projecteuclid.org/euclid.aos/1176324633


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