Convergence rates of orthogonal series regression estimators

• Autorzy: Waldemar Popiński
• Języki publikacji: EN

Abstrakty

EN

General conditions for convergence rates of nonparametric orthogonal series estimators of the regression function f(x)=E(Y | X = x) are considered. The estimators are obtained by the least squares method on the basis of a random observation sample (Y_i,X_i), i=1,...,n, where $X_i ∈ A ⊂ ℝ^d$ have marginal distribution with density $ϱ ∈ L^1(A)$ and Var( Y | X = x) is bounded on A. Convergence rates of the errors $E_X(f(X)-\widehat f_N(X))^2$ and $\Vert f-\widehat f_N\Vert_∞$ for the estimator $\widehat f_N(x) = \sum_{k=1}^N\widehat c_ke_k(x)$, constructed using an orthonormal system $e_k$, k=1,2,..., in $L^2(A)$ are obtained.

Słowa kluczowe

EN

orthonormal system; nonparametric series regression; least squares method; convergence rate

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2000
• Tom: 27
• Numer: 4
• Strony: 445-454

Daty

wydano

2000

otrzymano

1999-12-23

poprawiono

2000-07-31

Twórcy

autor

Waldemar Popiński

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

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