Hypotheses testing and posterior concentration rates for semi-Markov processes

被引：5
|
作者：
Votsi, I [1 ]
Gayraud, G. [2 ]
Barbu, V. S. [3 ]
Limnios, N. [2 ]
机构：
[1] Le Mans Univ, Inst Risque & Assurance, Lab Manceau Math LMM EA 3263, Ave Olivier Messiaen, F-72085 Le Mans 9, France
[2] Univ Technol Compiegne, LMAC Lab Appl Math Compiegne, CS 60 319, F-60203 Compiegne, France
[3] Univ Rouen Normandie, Lab Math Raphael Salem, UMR 6085, Ave Univ,BP 12, F-76801 St Etienne Du Rouvray, France
来源：
STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES | 2021年 / 24卷 / 03期
关键词：
Bayesian nonparametrics; Posterior concentration rates; Semi-Markov processes; Semi-Markov kernels; Robust statistical tests; BAYESIAN-ESTIMATION; DIRICHLET MIXTURES; CONVERGENCE-RATES; RENEWAL PROCESSES; SPECTRAL DENSITY; CONSISTENCY; MODELS;
D O I：
10.1007/s11203-021-09247-3
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
引用
收藏
页码：707 / 732
页数：26
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