Kvatadze, Zurab; Pharjiani, Beqnu Kernel estimations of the density distribution constructed by dependent observations and the accuracy of their approximation by \(L_1\) metric. (English) Zbl 1456.62060 Bull. Georgian Natl. Acad. Sci. (N.S.) 14, No. 1, 39-43 (2020). 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) Keywords:Markov chain; kernel estimate; conditionally independent sequence; sequence with chain dependence PDFBibTeX XMLCite \textit{Z. Kvatadze} and \textit{B. Pharjiani}, Bull. Georgian Natl. Acad. Sci. (N.S.) 14, No. 1, 39--43 (2020; Zbl 1456.62060) Full Text: Link