On statistics of Markov step processes: Representation of log-likelihood ratio processes in filtered local models

DOI10.1007/BF01199249zbMath0766.62051OpenAlexW2004862302MaRDI QIDQ1203944

Reinhard Hoepfner

Publication date: 18 February 1993

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01199249

zbMATH Keywords

local asymptotic normalitytrajectoryLANsequential sampling plansLAMNdecomposition of log-likelihood ratio processesfixed time samplingLAQMarkov step processscore function martingaleweak convergence of filtered local models

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Central limit and other weak theorems (60F05) Markov processes: estimation; hidden Markov models (62M05)

Related Items (10)

Nonparametric estimators for Markov step processes ⋮ Adaptive estimators for parameters of the autoregression function of a Markov chain ⋮ LAMN in a class of parametric models for null recurrent diffusions ⋮ Quasi-likelihood models and optimal inference ⋮ Optimality of estimators for misspecified semi-Markov models ⋮ Some developments in semiparametric statistics ⋮ Estimators for alternating nonlinear autoregression ⋮ Regularity of models associated with Markov jump processes ⋮ Information bounds for Gibbs samplers ⋮ Asymptotic inference for Markov step processes: Observation up to a random time

Cites Work

• Asymptotic optimal inference for non-ergodic models
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• On the strong approximation of the distributions of estimators in linear stochastic models, I and II: Stationary and explosive AR models
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• Convergence of filtered statistical models and Hellinger processes
• Local asymptotic normality and mixed normality for Markov statistical models
• Distribution of the Estimators for Autoregressive Time Series With a Unit Root
• Central limit theorems for local martingales
• Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales
• Some comments concerning a curious singularity
• A characterization of limiting distributions of regular estimates
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