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Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

Paper is devoted to estimation of conditional distribution function in heteroscedastical regression model, in which responses are α-mixing random variables. It is found the expression for mean square deviation of estimator and optimal window width sequence.

First Page

162

Last Page

167

References

1. Akritas M.G., Van Keilegom I. Nonparametric estimation of the residual estimation. Scandinavian Journal of Statistics, Vol. 28, Issue 3, 549–567 (2001).

2. Doukhan P. Mixing: Properties and Examples. Lecture Notes in Statistics, Vol. 85, Springer-Verlag, New York, (1994). – 144 pp.

3. Nadaraya E.A. Nonparametric estimation of probability density and regression curve. Tbilisi Univ. Publishing House, Tbilisi, (1983). – 194 pp. [in Russian].

4. Watson J.S. Smooth regression analysis. Sankhyā: The Indian Journal of Statistics, Series A, Vol. 26, No. 4, 359–372 (1964).

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