The properties of two recursive estimators of the Fourier coefficients of a regression function with respect to a complete orthonormal system of bounded functions (ek) , k=1,2,..., are considered in the case of the observation model , i=1,...,n , where are independent random variables with zero mean and finite variance, , i=1,...,n, form a random sample from a distribution with density ϱ =1/(b-a) (uniform distribution) and are independent of the errors , i=1,...,n . Unbiasedness and mean-square consistency of the examined estimators are proved and their mean-square errors are compared.
@article{bwmeta1.element.bwnjournal-article-zmv22z2p275bwm,
author = {Waldemar Popi\'nski},
title = {On Fourier coefficient estimators consistent in the mean-square sense},
journal = {Applicationes Mathematicae},
volume = {22},
year = {1994},
pages = {275-284},
zbl = {0801.62040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z2p275bwm}
}
Popiński, Waldemar. On Fourier coefficient estimators consistent in the mean-square sense. Applicationes Mathematicae, Tome 22 (1994) pp. 275-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z2p275bwm/
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