Geodesic
Convergence rates of orthogonal series regression estimators
Applicationes Mathematicae, Tome 27 (2000) no. 4, pp. 445-454 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am-27-4-445-454
Keywords: orthonormal system, nonparametric series regression, least squares method, convergence rate

Waldemar Popiński 1

1 
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Waldemar Popiński. Convergence rates of orthogonal series regression estimators. Applicationes Mathematicae, Tome 27 (2000) no. 4, pp. 445-454. doi: 10.4064/am-27-4-445-454

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