The Change-Point Problems

Abstract

In the following we consider several problems of parameter estimation in situations where the intensity functions have jumps and the corresponding families of measures are not LAN. The limits of the likelihood ratios contain the Poisson processes, and the properties of the MLE, BE, and MDE differ from the properties of these estimators as described in the preceding chapters. Particularly, the MLEs are no longer asymptotically efficient. We begin with the problem of joint estimation of a “smooth” parameter and an instant of jump. Then we describe the asymptotics of estimators in the so-called chess-field problem (including two-level intensity functions) and finally consider a problem of parametric curve estimation, when this curve is a boundary of discontinuity of intensity function.