Temat: nonparametric regression - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Orthogonal series regression estimators for an irregularly spaced design
Autorzy:: Popiński, Waldemar
Powiązania:: https://bibliotekanauki.pl/articles/1208167.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: convergence rates
nonparametric regression
orthogonal series estimator
Opis:: Nonparametric orthogonal series regression function estimation is investigated in the case of a fixed point design where the observation points are irregularly spaced in a finite interval [a,b]i ⊂ ℝ. Convergence rates for the integrated mean-square error and pointwise mean-square error are obtained in the case of estimators constructed using the Legendre polynomials and Haar functions for regression functions satisfying the Lipschitz condition.
Źródło:: Applicationes Mathematicae; 2000, 27, 3; 309-318
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A note on orthogonal series regression function estimators
Autorzy:: Popiński, Waldemar
Powiązania:: https://bibliotekanauki.pl/articles/1338775.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: consistent estimator
orthonormal system
empirical risk minimization
nonparametric regression
Opis:: The problem of nonparametric estimation of the regression function f(x) = E(Y | X=x) using the orthonormal system of trigonometric functions or Legendre polynomials $e_k$, k=0,1,2,..., is considered in the case where a sample of i.i.d. copies $(X_i,Y_i)$, i=1,...,n, of the random variable (X,Y) is available and the marginal distribution of X has density ϱ ∈ $L^1$[a,b]. The constructed estimators are of the form $\widehat f_n(x) = \sum_{k=0}^{N(n)}\widehat c_ke_k(x)$, where the coefficients $\widehat c_0,\widehat c_1,...,\widehat c_N$ are determined by minimizing the empirical risk $n^{-1}\sum_{i=1}^n(Y_i - \sum_{k=0}^Nc_ke_k(X_i))^2$. Sufficient conditions for consistency of the estimators in the sense of the errors $E_X\vert f(X)-\widehat f_n(X)\vert^2$ and $n^{-1}\sum_{i=1}^nE(f(X_i)-\widehat f_n(X_i))^2$ are obtained.
Źródło:: Applicationes Mathematicae; 1999, 26, 3; 281-291
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

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

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