Hypothesis testing for Markovian models with random time observations

The aim of this paper is to propose a methodology for testing general hypotheses in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals τk, assumed to be i.i.d. with unknown distribution μ. 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 μ, 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.