Robust inference in generalized Ornstein-Uhlenbeck processes with multiple change-points
Severien Nkurunziza, Department of Mathematics and Statistics, The University of Windsor, Canada
In this talk, we present improved inference methods in generalized Ornstein-Uhlenbeck processes with multiple unknown change-points when the drift parameter satisfies uncertain constraint. A Salient feature of this 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) and we derive their asymptotic properties. Third, we derive a test for testing the hypothesized restriction 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. The novelty of the established results 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 the results in statistical literature