Orthogonal series estimation of band-limited regression functions

Waldemar Popiński

Applicationes Mathematicae, Volume 41 (2014), p. 51-65 / Harvested from The Polish Digital Mathematics Library

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 $f ̂ ₙ (x) = \sum_{k = - N (n)}^{N (n)} c ̂_{k} s_{k} (x)$ with coefficients $c ̂_{k}$ , k = -N(n),...,N(n), obtained by the Monte Carlo method are studied.

Published online : 2014-01-01

Zbl 1298.62066

EUDML-ID : urn:eudml:doc:280071

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     author = {Waldemar Popi\'nski},
     title = {Orthogonal series estimation of band-limited regression functions},
     journal = {Applicationes Mathematicae},
     volume = {41},
     year = {2014},
     pages = {51-65},
     zbl = {1298.62066},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-5}
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Waldemar Popiński. Orthogonal series estimation of band-limited regression functions. Applicationes Mathematicae, Volume 41 (2014) pp. 51-65. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-5/