Orthogonal series regression estimation under long-range dependent errors

Waldemar Popiński

Applicationes Mathematicae, Tome 28 (2001), p. 457-466 / Harvested from The Polish Digital Mathematics Library

Résumé

This paper is concerned with general conditions for convergence rates of nonparametric orthogonal series estimators of the regression function. The estimators are obtained by the least squares method on the basis of an observation sample $Y_{i} = f (X_{i}) + η_{i}$ , i=1,...,n, where $X_{i} \in A \subset ℝ^{d}$ are independently chosen from a distribution with density ϱ ∈ L¹(A) and $η_{i}$ are zero mean stationary errors with long-range dependence. Convergence rates of the error $n^{- 1} \sum_{i = 1}^{n} (f (X_{i}) - f ̂_{N} (X_{i})) ²$ for the estimator $f ̂_{N} (x) = \sum_{k = 1}^{N} c ̂_{k} e_{k} (x)$ , constructed using an orthonormal system $e_{k}$ , k=1,2,..., in L²(A), are obtained.

Publié le : 2001-01-01

Zbl 1008.62577

EUDML-ID : urn:eudml:doc:279548

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     author = {Waldemar Popi\'nski},
     title = {Orthogonal series regression estimation under long-range dependent errors},
     journal = {Applicationes Mathematicae},
     volume = {28},
     year = {2001},
     pages = {457-466},
     zbl = {1008.62577},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-4-6}
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Waldemar Popiński. Orthogonal series regression estimation under long-range dependent errors. Applicationes Mathematicae, Tome 28 (2001) pp. 457-466. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-4-6/