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Strong consistency of Kernel density estimates for Markov chains failure rates

Authors:	G S Atuncar C C Y Dorea C R Gonçalves

Institution:	(1) Depto. de Estatística, ICEX, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte-MG, Brazil;(2) Depto. de Matemática, Universidade de Brasília, 70910-900 Brasília-DF, Brazil

Abstract:	For a homogeneous and uniformly ergodic Markov chain, with transition kernel $P(x, A) = \int_{A} f(y\|x)\hbox{d}y, x \in E \subset R^{d}$ , we analyse some reliability measures and failure rates associated with the transition probabilities. Sufficient conditions for strong consistency are obtained for estimates based on kernel density estimators.

Keywords:	Failure rates for Markov chain Kernel density estimators
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