# Convergence rates of orthogonal series regression estimators

Applicationes Mathematicae (2000)

- Volume: 27, Issue: 4, page 445-454
- ISSN: 1233-7234

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topPopiński, Waldemar. "Convergence rates of orthogonal series regression estimators." Applicationes Mathematicae 27.4 (2000): 445-454. <http://eudml.org/doc/219287>.

@article{Popiński2000,

abstract = {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 $X_i ∈ A ⊂ ℝ^d$ have marginal distribution with density $ϱ ∈ L^1(A)$ and Var( Y | X = x) is bounded on A. Convergence rates of the errors $E_X(f(X)-\widehat\{f\}_N(X))^2$ and $\Vert f-\widehat\{f\}_N\Vert _∞$ for the estimator $\widehat\{f\}_N(x) = \sum _\{k=1\}^N\widehat\{c\}_ke_k(x)$, constructed using an orthonormal system $e_k$, k=1,2,..., in $L^2(A)$ are obtained.},

author = {Popiński, Waldemar},

journal = {Applicationes Mathematicae},

keywords = {orthonormal system; nonparametric series regression; least squares method; convergence rate},

language = {eng},

number = {4},

pages = {445-454},

title = {Convergence rates of orthogonal series regression estimators},

url = {http://eudml.org/doc/219287},

volume = {27},

year = {2000},

}

TY - JOUR

AU - Popiński, Waldemar

TI - Convergence rates of orthogonal series regression estimators

JO - Applicationes Mathematicae

PY - 2000

VL - 27

IS - 4

SP - 445

EP - 454

AB - 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 $X_i ∈ A ⊂ ℝ^d$ have marginal distribution with density $ϱ ∈ L^1(A)$ and Var( Y | X = x) is bounded on A. Convergence rates of the errors $E_X(f(X)-\widehat{f}_N(X))^2$ and $\Vert f-\widehat{f}_N\Vert _∞$ for the estimator $\widehat{f}_N(x) = \sum _{k=1}^N\widehat{c}_ke_k(x)$, constructed using an orthonormal system $e_k$, k=1,2,..., in $L^2(A)$ are obtained.

LA - eng

KW - orthonormal system; nonparametric series regression; least squares method; convergence rate

UR - http://eudml.org/doc/219287

ER -

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