Misspecified change-point estimation problem for a Poisson process
| Autor: | Yury A. Kutoyants, Ali S. Dabye |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Statistics and Probability
Estimation theory General Mathematics Function (mathematics) Poisson distribution Combinatorics Moment (mathematics) symbols.namesake Statistics Compound Poisson process symbols Zero-inflated model Point estimation Statistics Probability and Uncertainty Fractional Poisson process Mathematics |
| Zdroj: | Journal of Applied Probability. 38:122-130 |
| ISSN: | 1475-6072 0021-9002 |
| DOI: | 10.1239/jap/1085496596 |
| Popis: | Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗ to an upper function h∗ at some unknown point θ ∗. What is known are continuous bounding functions g and h such that g∗ (t) ≤ g(t) ≤ h(t) ≤ h∗ (t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ ∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗ and h ∗. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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