Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
275-284
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-03-04
Twórcy
autor
- Research and Development Center of Statistics, al. Niepodległości 208, 00-925 Warszawa, Poland
Bibliografia
- [1] A. E. Albert and L. A. Gardner, Stochastic Approximation and Nonlinear Regression, Cambridge Univ. Press, 1967.
- [2] J. Koronacki, Stochastic Approximation-Optimization Methods under Random Conditions, WNT, Warszawa, 1989 (in Polish).
- [3] E. A. Nadaraya, Nonparametric Estimation of Probability Densities and Regression Curves, Kluwer Acad. Publ., Dordrecht, 1989.
- [4] G. Sansone, Orthogonal Functions, Interscience, New York, 1959.
- [5] A. Zygmund, Trigonometrical Series, Dover, 1955.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv22z2p275bwm