Statistical Estimation of Ergodic Markov Chain Kernel over Discrete State Space
Abstract
We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax sample complexity of estimation with respect to the operator infinity norm, while in the countably infinite case, we analyze the problem with respect to a natural entry-wise norm derived from total variation. We show that in both cases, the sample complexity is governed by the mixing properties of the unknown chain, for which, in the finite-state case, there are known finite-sample estimators with fully empirical confidence intervals.
Keywords
Cite
@article{arxiv.1809.05014,
title = {Statistical Estimation of Ergodic Markov Chain Kernel over Discrete State Space},
author = {Geoffrey Wolfer and Aryeh Kontorovich},
journal= {arXiv preprint arXiv:1809.05014},
year = {2020}
}
Comments
Journal version of the extended abstract (ALT'19), to appear in Bernoulli 2020+