Orthogonal series estimation of band-limited regression functions

• Autorzy: Waldemar Popiński
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 62F12: Asymptotic properties of estimators
• 62G08: Nonparametric regression

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2014
• Tom: 41
• Numer: 1
• Strony: 51-65

Daty

wydano

2014

Twórcy

autor

Waldemar Popiński

• Space Research Centre, Polish Academy of Sciences, Bartycka 18a, 00-716 Warszawa, Poland

Identyfikatory

DOI

10.4064/am41-1-5