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Kernel estimations of the density distribution constructed by dependent observations and the accuracy of their approximation by \(L_1\) metric. (English) Zbl 1456.62060

Summary: Kernel estimations of the Rosenblatt-Parzen type of unknown density distribution by conditionally independent and chain-dependent observations are constructed. The upper boundaries for the approximations of these densities constructed by estimates for \(L_1\) metric are determined. The obtained results are specified for the case of Bartlett kernel and smoothing coefficient \(a_n=\sqrt n\).

MSC:

62G07 Density estimation
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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