Abstract

In this talk, we present some inference methods in generalized Ornstein-Uhlenbeck processes with multiple unknown change-points when the drift parameter may satisfy uncertain restriction. A Salient feature of this statistical investigation consists in the fact that the number of change-points and the locations of the change-points are unknown. We generalize some recent findings in five ways. First, our inference method incorporates the uncertain prior knowledge. Second, we derive the unrestricted estimator (UE) and the restricted estimator (RE) as well as their asymptotic properties. Third, we establish a test for testing the hypothesized constraint and we derive its asymptotic power. Fourth, we propose a class of shrinkage estimators (SEs) which includes as special cases the UE, RE, and classical SEs. Fifth, we study the relative risk dominance of the proposed estimators, and we establish that SEs dominate the UE and the RE performs very well in the neighbourhood of the restriction, but this performs poorly when the restriction is seriously violated. The additional novelty of the established methods consists in the fact that the dimensions of the proposed estimators are random. Because of that, the asymptotic power of the proposed test and the asymptotic risk analysis do not follow from classical results in statistical literature. To overcome this problem, we establish an asymptotic result which is useful in its own.