Hypothesis testing for markovian models with random time observations

TL;DR

This paper introduces new statistical tests for Markov chains observed at random times, enabling hypothesis testing on transition structures and time gap distributions, with proven consistency and demonstrated effectiveness through simulations.

Contribution

It proposes novel testing procedures for Markov models with random sampling, including affine constraints on transition matrices and goodness-of-fit for time gaps, with theoretical validation.

Findings

Tests are consistent under mild assumptions.

Methodologies perform well in simulations.

Applicable to various Markovian models with random sampling.

Abstract

The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown distribution $\mu$. Two test procedures are investigated. The first one is devoted to testing if the transition matrix P of the Markov chain X satisfies specific affine constraints, covering a wide range of situations such as symmetry or sparsity. The second procedure is a goodness-of-fit test on the distribution $\mu$, which reveals to be consistent under mild assumptions even though the time gaps are not observed. The theoretical results are supported by a Monte Carlo simulation study to show the performance and robustness of the proposed methodologies on specific numerical examples.