Geodesic
Convergence rates of orthogonal series regression estimators
Applicationes Mathematicae, Tome 27 (2000) no. 4, pp. 445-454

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI Zbl  

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 (Y_i,X_i), 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.
DOI : 10.4064/am-27-4-445-454
Keywords: orthonormal system, nonparametric series regression, least squares method, convergence rate 
Waldemar Popiński. Convergence rates of orthogonal series regression estimators. Applicationes Mathematicae, Tome 27 (2000) no. 4, pp. 445-454. doi: 10.4064/am-27-4-445-454
@article{10_4064_am_27_4_445_454,
     author = {Waldemar Popi\'nski},
     title = {Convergence rates of orthogonal series regression estimators},
     journal = {Applicationes Mathematicae},
     pages = {445--454},
     year = {2000},
     volume = {27},
     number = {4},
     doi = {10.4064/am-27-4-445-454},
     zbl = {0992.62040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-27-4-445-454/}
}
TY  - JOUR
AU  - Waldemar Popiński
TI  - Convergence rates of orthogonal series regression estimators
JO  - Applicationes Mathematicae
PY  - 2000
SP  - 445
EP  - 454
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-27-4-445-454/
DO  - 10.4064/am-27-4-445-454
LA  - en
ID  - 10_4064_am_27_4_445_454
ER  - 
%0 Journal Article
%A Waldemar Popiński
%T Convergence rates of orthogonal series regression estimators
%J Applicationes Mathematicae
%D 2000
%P 445-454
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4064/am-27-4-445-454/
%R 10.4064/am-27-4-445-454
%G en
%F 10_4064_am_27_4_445_454

Cité par Sources :