Orthogonal series regression estimation under long-range dependent errors

Waldemar Popiński. "Orthogonal series regression estimation under long-range dependent errors." Applicationes Mathematicae 28.4 (2001): 457-466. <http://eudml.org/doc/279548>.

@article{WaldemarPopiński2001,
abstract = {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 $X_i ∈ A ⊂ ℝ^d$ 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 $n^\{-1\} ∑_\{i=1\}^n (f(X_i)-f̂_N(X_i))²$ for the estimator $f̂_N(x) = ∑_\{k=1\}^N ĉ_k e_k(x)$, constructed using an orthonormal system $e_k$, k=1,2,..., in L²(A), are obtained.},
author = {Waldemar Popiński},
journal = {Applicationes Mathematicae},
keywords = {nonparametric series regression; least squares method; orthonormal system; convergence rate},
language = {eng},
number = {4},
pages = {457-466},
title = {Orthogonal series regression estimation under long-range dependent errors},
url = {http://eudml.org/doc/279548},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Waldemar Popiński
TI - Orthogonal series regression estimation under long-range dependent errors
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 4
SP - 457
EP - 466
AB - 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 $X_i ∈ A ⊂ ℝ^d$ 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 $n^{-1} ∑_{i=1}^n (f(X_i)-f̂_N(X_i))²$ for the estimator $f̂_N(x) = ∑_{k=1}^N ĉ_k e_k(x)$, constructed using an orthonormal system $e_k$, k=1,2,..., in L²(A), are obtained.
LA - eng
KW - nonparametric series regression; least squares method; orthonormal system; convergence rate
UR - http://eudml.org/doc/279548
ER -