On Bayesian estimators in misspecified change-point problems for Poisson process

✍ Scribed by Ali S. Dabye; Christian Farinetto; Yury A. Kutoyants

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 164 KB
• Volume: 61
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(02)00200-6

✦ Synopsis

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 # * . Here, # * is a random variable. What is known are continuous bounding functions g and h such that g * (t) 6 g(t) ¡ h(t) 6 h * (t) for 0 6 t 6 T and the prior density function of #. It is shown that on the basis of n observations of the process X the Bayesian estimator #n of # * is consistent for n → ∞, and also that n( #n -# * ) converges in law and in p th moment to limits described in terms of the unknown functions g * and h * .