On Fourier coefficient estimators consistent in the mean-square sense

• Autorzy: Waldemar Popiński
• Języki publikacji: EN

Abstrakty

EN

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

EN

unbiasedness; consistent estimator; Fourier coefficients; mean-square error

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1993-1995
• Tom: 22
• Numer: 2
• Strony: 275-284

Daty

wydano

1994

otrzymano

1993-03-04

Twórcy

autor

Waldemar Popiński

• 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.