NONPARAMETRIC ESTIMATION IN MARKOV PROCESSES.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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The purpose of the present paper is to consider the non-parametric estimation of densities in the case of Markov processes. Asymptotically unbiased estimates for the initial and two-dimensional joint densities are constructed. These estimates are shown to be consistent in quadratic mean, and furthermore a consistent, in the probability sense, estimate for the transition density is obtained. It is shown that, under suitable conditions, all three estimators mentioned, properly normalized, are asymptotically normal.
- Statistics and Probability