Convergence rates of orthogonal series regression estimators

Popiński, Waldemar

Applicationes Mathematicae, Tome 27 (2000), p. 445-454 / Harvested from The Polish Digital Mathematics Library

Résumé

General conditions for convergence rates of nonparametric orthogonal series estimators of the regression function f(x)=E(Y | X = x) are considered. The estimators are obtained by the least squares method on the basis of a random observation sample (Yi,Xi), i=1,...,n, where $X_{i} \in A \subset ℝ^{d}$ have marginal distribution with density $ϱ \in L^{1} (A)$ and Var( Y | X = x) is bounded on A. Convergence rates of the errors $E_{X} {(f (X) - {\hat{f}}_{N} (X))}^{2}$ and $∥ f - {\hat{f}}_{N} ∥_{\infty}$ for the estimator ${\hat{f}}_{N} (x) = \sum_{k = 1}^{N} {\hat{c}}_{k} e_{k} (x)$ , constructed using an orthonormal system $e_{k}$ , k=1,2,..., in $L^{2} (A)$ are obtained.

Publié le : 2000-01-01

Zbl 0992.62040

EUDML-ID : urn:eudml:doc:219287

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     author = {Waldemar Popi\'nski},
     title = {Convergence rates of orthogonal series regression estimators},
     journal = {Applicationes Mathematicae},
     volume = {27},
     year = {2000},
     pages = {445-454},
     zbl = {0992.62040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p445bwm}
}

Popiński, Waldemar. Convergence rates of orthogonal series regression estimators. Applicationes Mathematicae, Tome 27 (2000) pp. 445-454. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p445bwm/

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