Orthogonal series regression estimation under long-range dependent errors

• Autorzy: Waldemar Popiński
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 62G20: Asymptotic properties
• 62G08: Nonparametric regression

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2001
• Tom: 28
• Numer: 4
• Strony: 457-466

Daty

wydano

2001

Twórcy

autor

Waldemar Popiński

• Department of Survey Design, Central Statistical Office, Al. Niepodległości 208, 00-925 Warszawa, Poland

Identyfikatory

DOI

10.4064/am28-4-6