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Applicationes Mathematicae

2014 | 41 | 1 | 51-65

Orthogonal series estimation of band-limited regression functions

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.

51-65

wydano
2014

Twórcy

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