On limiting likelihood ratio processes of some change-point type statistical models

Different change-point type models encountered in parametric statistical inference give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an exponential functional of a two-sided Poisson process driven by some parameter, whi...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2010-09, Vol.140 (9), p.2682-2692
Main Author: Dachian, Sergueï
Format: Article
Language:English
Subjects:
Asymptotic efficiency
Bayesian estimators
Change-point
Exact sciences and technology
General topics
Limiting distribution
Limiting likelihood ratio process
Limiting variance
Markov processes
Mathematics
Maximum likelihood estimator
Non-regularity
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Statistics Theory
Stochastic processes
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Summary:Different change-point type models encountered in parametric statistical inference give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an exponential functional of a two-sided Poisson process driven by some parameter, while the second one is an exponential functional of a two-sided Brownian motion. We establish that for sufficiently small values of the parameter, the Poisson type likelihood ratio can be approximated by the Brownian type one. As a consequence, several statistically interesting quantities (such as limiting variances of different estimators) related to the first likelihood ratio can also be approximated by those related to the second one. Finally, we discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.03.030