Nonparametric estimation of the stationary density and the transition density of a Markov chain

Claire Lacour

Stochastic Processes and their Applications, 2008, vol. 118, issue 2, 232-260

Abstract: In this paper, we study first the problem of nonparametric estimation of the stationary density f of a discrete-time Markov chain (Xi). We consider a collection of projection estimators on finite dimensional linear spaces. We select an estimator among the collection by minimizing a penalized contrast. The same technique enables us to estimate the density g of (Xi,Xi+1) and so to provide an adaptive estimator of the transition density [pi]=g/f. We give bounds in L2 norm for these estimators and we show that they are adaptive in the minimax sense over a large class of Besov spaces. Some examples and simulations are also provided.

Keywords: Adaptive; estimation; Markov; chain; Stationary; density; Transition; density; Model; selection; Penalized; contrast; Projection; estimators (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (10)

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