Explicit limit results for minimal sufficient statistics and maximum likelihood estimators in some Markov processes: Exponential families approach

DOI10.1214/aos/1176324699zbMath0852.62076OpenAlexW2033001102MaRDI QIDQ1906202

Valeri T. Stefanov

Publication date: 12 November 1996

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176324699

zbMATH Keywords

asymptotic normalityfunctional central limit theoremsMarkov renewal processesmaximum likelihood estimatorsstopping timesMarkov-additive processesfinite-state Markov chainslimit resultscurved exponential familieslikelihood functionsminimal sufficient statisticsfunctional laws of iterated logarithmvariance parameter

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic distribution theory in statistics (62E20) Markov processes: estimation; hidden Markov models (62M05) Functional limit theorems; invariance principles (60F17) Sequential estimation (62L12)

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Information geometry approach to parameter estimation in Markov chains ⋮ Parameter estimation for switched counting processes ⋮ Explicit distributional results in pattern formation ⋮ Exact distributions for reward functions on semi-Markov and Markov additive processes ⋮ Variance estimation in the central limit theorem for Markov chains ⋮ Information geometry of reversible Markov chains ⋮ On run statistics for binary trials

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