Hypotheses testing and posterior concentration rates for semi-Markov processes

I. Votsi (), G. Gayraud, V. S. Barbu and N. Limnios
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I. Votsi: Institut du Risque et de l’Assurance, Le Mans Université
G. Gayraud: Université de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne)
V. S. Barbu: Université de Rouen-Normandie, UMR 6085
N. Limnios: Université de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne)

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 3, No 7, 707-732

Abstract: Abstract In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous-time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and countable state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates.

Keywords: Bayesian nonparametrics; Posterior concentration rates; Semi-Markov processes; Semi-Markov kernels; Robust statistical tests (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09247-3

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DOI: 10.1007/s11203-021-09247-3

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