- Tytuł:
- On Fourier coefficient estimators consistent in the mean-square sense
- Autorzy:
- Popiński, Waldemar
- Powiązania:
- https://bibliotekanauki.pl/articles/1340627.pdf
- Data publikacji:
- 1994
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
unbiasedness
consistent estimator
Fourier coefficients
mean-square error - Opis:
- The properties of two recursive estimators of the Fourier coefficients of a regression function $f \in L^2[a,b]$ with respect to a complete orthonormal system of bounded functions (e_k) , k=1,2,..., are considered in the case of the observation model $y_i = f(x_i) + η_i$, i=1,...,n , where $η_i$ are independent random variables with zero mean and finite variance, $x_i \in [a,b] \subset {\sym R}^1$, i=1,...,n, form a random sample from a distribution with density ϱ =1/(b-a) (uniform distribution) and are independent of the errors $η_i$, i=1,...,n . Unbiasedness and mean-square consistency of the examined estimators are proved and their mean-square errors are compared.
- Źródło:
-
Applicationes Mathematicae; 1993-1995, 22, 2; 275-284
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł