On the occupancy problem for a regime switching model

Abstract

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching Markov chain. For this model, we 1) give finite sample bounds on the occupancy probabilities, and 2) provide detailed asymptotics in the case where the underlying distribution is regularly varying. We find that, in the regularly varying case, the finite sample bounds are rate optimal and have, up to a constant, the same rate of decay as the asymptotic result.

References in corpus (4)

• General state space Markov chains and MCMC algorithms
• Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws
• Estimation of sums of random variables: Examples and information bounds
• Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications