Efficient estimation of the stationary distribution for exponentially ergodic Markov chains
type: Item
instance of: scholarly article
title: Efficient estimation of the stationary distribution for exponentially ergodic Markov chains
zbMATH Open document ID: 0727.62079
DOI: 10.1016/0378-3758(91)90085-S
published in: Journal of Statistical Planning and Inference
publication date: 1991-01-01T00:00:00Z
review text: The paper deals with the problem of estimation of the unknown continuous stationary distribution F of a stationary and ergodic random sequence \(X_ 1,X_ 2,... \). In this case, the empirical distribution function \(\hat F_ n\) still can be used. However, another serious problem arises, that of the asymptotic efficiency of \(\hat F_ n.\) The author has given an affirmative solution to the last problem. The exponential ergodicity of the Markov sequence \(X_ n\), \(n\geq 1\), is among the additional conditions under which it is shown that \(\hat F_ n\) is locally asymptotically minimax. Moreover, the local minimax bound is calculated explicitly. As a whole, this well written paper is a nice contribution to the temporary topic ``Inference for stochastic processes''.
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 4201424
zbMATH Keywords: stability
zbMATH Keywords: continuous stationary distribution
zbMATH Keywords: stationary and ergodic random sequence
zbMATH Keywords: empirical distribution
zbMATH Keywords: asymptotic efficiency
zbMATH Keywords: exponential ergodicity
zbMATH Keywords: Markov sequence
zbMATH Keywords: locally asymptotically minimax
zbMATH Keywords: local minimax bound
author: Spiridon Penev
reviewed by: Jordan Stoyanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4201424