Orthogonal series estimation of band-limited regression functions

Waldemar Popiński. "Orthogonal series estimation of band-limited regression functions." Applicationes Mathematicae 41.1 (2014): 51-65. <http://eudml.org/doc/280071>.

@article{WaldemarPopiński2014,
abstract = {The problem of nonparametric function fitting using the complete orthogonal system of Whittaker cardinal functions $s_k$, k = 0,±1,..., for the observation model $y_j = f(u_j) + η_j$, j = 1,...,n, is considered, where f ∈ L²(ℝ) ∩ BL(Ω) for Ω > 0 is a band-limited function, $u_j$ are independent random variables uniformly distributed in the observation interval [-T,T], $η_j$ are uncorrelated or correlated random variables with zero mean value and finite variance, independent of the observation points. Conditions for convergence and convergence rates of the integrated mean-square error E||f-f̂ₙ||² and the pointwise mean-square error E(f(x)-f̂ₙ(x))² of the estimator $f̂ₙ(x) = ∑_\{k=-N(n)\}^\{N(n)\} ĉ_k s_k(x)$ with coefficients $ĉ_k$, k = -N(n),...,N(n), obtained by the Monte Carlo method are studied.},
author = {Waldemar Popiński},
journal = {Applicationes Mathematicae},
keywords = {band-limited function; orthogonal series; expansion coefficients; regression function; consistent estimator; convergence rate},
language = {eng},
number = {1},
pages = {51-65},
title = {Orthogonal series estimation of band-limited regression functions},
url = {http://eudml.org/doc/280071},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Waldemar Popiński
TI - Orthogonal series estimation of band-limited regression functions
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 1
SP - 51
EP - 65
AB - The problem of nonparametric function fitting using the complete orthogonal system of Whittaker cardinal functions $s_k$, k = 0,±1,..., for the observation model $y_j = f(u_j) + η_j$, j = 1,...,n, is considered, where f ∈ L²(ℝ) ∩ BL(Ω) for Ω > 0 is a band-limited function, $u_j$ are independent random variables uniformly distributed in the observation interval [-T,T], $η_j$ are uncorrelated or correlated random variables with zero mean value and finite variance, independent of the observation points. Conditions for convergence and convergence rates of the integrated mean-square error E||f-f̂ₙ||² and the pointwise mean-square error E(f(x)-f̂ₙ(x))² of the estimator $f̂ₙ(x) = ∑_{k=-N(n)}^{N(n)} ĉ_k s_k(x)$ with coefficients $ĉ_k$, k = -N(n),...,N(n), obtained by the Monte Carlo method are studied.
LA - eng
KW - band-limited function; orthogonal series; expansion coefficients; regression function; consistent estimator; convergence rate
UR - http://eudml.org/doc/280071
ER -