- Tytuł:
- Convergence rates of orthogonal series regression estimators
- Autorzy:
- Popiński, Waldemar
- Powiązania:
- https://bibliotekanauki.pl/articles/1208155.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
orthonormal system
nonparametric series regression
least squares method
convergence rate - Opis:
- 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.
- Źródło:
-
Applicationes Mathematicae; 2000, 27, 4; 445-454
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł