Efficient estimation of the stationary distribution for exponentially ergodic Markov chains
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''.
scientific article; zbMATH DE number 4201424
scientific article