Hypotheses testing and posterior concentration rates for semi-Markov processes

被引：0
作者：
I. Votsi
G. Gayraud
V. S. Barbu
N. Limnios
机构：
[1] Institut du Risque et de l’Assurance,Laboratoire Manceau de Mathématiques
[2] Le Mans Université, LMM EA 3263
[3] Université de Technologie de Compiègne,Laboratoire de Mathématiques Raphaël Salem
[4] LMAC (Laboratory of Applied Mathematics of Compiègne),undefined
[5] Université de Rouen-Normandie,undefined
[6] UMR 6085,undefined
来源：
Statistical Inference for Stochastic Processes | 2021年 / 24卷
关键词：
Bayesian nonparametrics; Posterior concentration rates; Semi-Markov processes; Semi-Markov kernels; Robust statistical tests;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：707 / 732
页数：25
相关论文
共 65 条
  • [21] Hsiung CA(1992)Convergence of estimates under dimensionality restrictions J Soviet Math 18 603-616
  • [22] Choudhuri N(2013)Asymptotic optimality of criteria in the problem of testing hypotheses for a recurrent semi-Markov process J Multiv Anal 32 1231-1242
  • [23] Ghosal S(1990)Posterior consistency in conditional distribution estimation Ann Stat 32 1243-1259
  • [24] Roy A(1961)Bayes estimation from a Markov renewal process Ann Math Stat 40 964-995
  • [25] Çinlar E(1961)Markov renewal processes: definitions and preliminary properties Ann Math Stat 232 6-31
  • [26] Economou T(2012)Markov renewal processes with finitely many states Ann Stat 29 687-714
  • [27] Bailey TC(1955)Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process Proc R Soc Lond Ser A 3 115-128
  • [28] Kapelan Z(2001)Regenerative stochastic processes Ann Stat 137 1711-1726
  • [29] Epifani I(1954)Rates of convergence of posterior distributions Magyar Tud Akad Mat Kutato Int Közl 3 281-286
  • [30] Ladelli L(2007)Some investigations concerning recurrent stochastic processes of a certain type J Statist Plann Inference undefined undefined-undefined
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