The problem of estimation of a distribution function is considered in the case where the observer has access only to a part of the indicator random values. Some basic asymptotic properties of the constructed estimates are studied. The limit theorems are proved for continuous functionals related to the estimation of \( {\hat{F}_n}(x) \) in the space C[a, 1 - a], 0 < a < 1/2.
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References
K. V. Mandzhgaladze, “On an estimator of a distribution function and its moments,” Soobshch. Akad. Nauk Gruz. SSR, 124, No. 2, 261–263 (1986).
E. Parzen, “On estimation of a probability density function and mode,” Ann. Math. Statist., 33, 1065–1076 (1962).
P. Whittle, “Bounds for the moments of linear and quadratic forms in independent variables,” Teor. Ver. Primen., 5, 331–335 (1960).
I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes [in Russian], Fizmatgiz, Moscow (1965).
A. V. Ivanov, “Properties of a nonparametric estimate of the regression function,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 499–502, 589 (1979).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1642–1658, December, 2010.
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Nadaraya, E., Babilua, P. & Sokhadze, G. Estimation of a distribution function by an indirect sample. Ukr Math J 62, 1906–1924 (2011). https://doi.org/10.1007/s11253-011-0479-y
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DOI: https://doi.org/10.1007/s11253-011-0479-y