- Tytuł:
- Least-squares trigonometric regression estimation
- Autorzy:
- Popiński, Waldemar
- Powiązania:
- https://bibliotekanauki.pl/articles/1338814.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
consistent estimator
least squares method
Fourier coefficients
trigonometric polynomial
regression function - Opis:
- The problem of nonparametric function fitting using the complete orthogonal system of trigonometric functions $e_k$, k=0,1,2,..., for the observation model $y_i = f(x_{in}) + η_i$, i=1,...,n, is considered, where $η_i$ are uncorrelated random variables with zero mean value and finite variance, and the observation points $x_{in} ∈ [0,2π]$, i=1,...,n, are equidistant. Conditions for convergence of the mean-square prediction error $(1/n)\sum_{i=1}^n E(f(x_{in})-\widehat f_{N(n)}(x_{in}))^2$, the integrated mean-square error $E ‖f-\widehat f_{N(n)}‖^2$ and the pointwise mean-square error $E(f(x)-\widehatf_{N(n)}(x))^2$ of the estimator $\widehat f_{N(n)}(x) = \sum_{k=0}^{N(n)} \widehat c_k e_k(x)$ for f ∈ C[0,2π] and $\widehat c_0,\widehat c_1,...,\widehat c_{N(n)}$ obtained by the least squares method are studied.
- Źródło:
-
Applicationes Mathematicae; 1999, 26, 2; 121-131
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł