Nonparametric Regression Under Long-Range Dependent Normal Errors

Csorgo, Sandor; Mielniczuk, Jan

Ann. Statist., Tome 23 (1995) no. 6, p. 1000-1014 / Harvested from Project Euclid

Résumé

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.

Publié le : 1995-06-14
Classification: Long-range dependence, kernel regression estimators, fixed design, maximal deviations, finite-dimensional distributions, 62G07, 62M99, 60F17

@article{1176324633,
     author = {Csorgo, Sandor and Mielniczuk, Jan},
     title = {Nonparametric Regression Under Long-Range Dependent Normal Errors},
     journal = {Ann. Statist.},
     volume = {23},
     number = {6},
     year = {1995},
     pages = { 1000-1014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176324633}
}

Csorgo, Sandor; Mielniczuk, Jan. Nonparametric Regression Under Long-Range Dependent Normal Errors. Ann. Statist., Tome 23 (1995) no. 6, pp.  1000-1014. http://gdmltest.u-ga.fr/item/1176324633/