Rejoinder on: Extensions of some classical methods in change point analysis

Abstract

The task of surveying a field as rich as change point analysis is difficult, if not impossible, to accomplish with a single paper. Therefore, to begin this rejoinder, wewould like to thank the discussants for their insightful and valuable contributions in the form of comments on our paper. Many aspects of change point analysis which did not appear in our paper, or received little attention, have been given consideration and further references in the comments. Moreover, the points raised in the discussions illustrate the cutting edge of modern change point analysis and avenues for future research. Below we respond to the comments of each discussant individually and suggest related open problems. ProfessorsHuskova andPraskova focused their discussion on robust tests for change point detection, and they provided several references where robust estimators are used. So far univariate observations and parameters have comprised the bulk of the literature in this direction. Based on the comments of Professors Huskova and Praskova, it would be interesting and practical to consider the multivariate and infinite dimensional cases. This is a difficult question froma theoretical point of view. Presently, to our knowledge, not a single paper has been devoted to the effect of outliers in functional data. The estimation of the covariance function and the long run covariance function are average