Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1150255 | Journal of Statistical Planning and Inference | 2010 | 11 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sergueï Dachian,