Title | ASYMPTOTICS FOR CHANGE-POINT MODELS UNDER VARYING DEGREES OF MIS-SPECIFICATION. |
Publication Type | Journal Article |
Year of Publication | 2016 |
Authors | Song, Rui, Moulinath Banerjee, and Michael R. Kosorok |
Journal | Ann Stat |
Volume | 44 |
Issue | 1 |
Pagination | 153-182 |
Date Published | 2016 Feb |
ISSN | 0090-5364 |
Abstract | Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate () and are asymptotically described by minimizers of a jump process. Under complete mis-specification by a smooth curve, i.e. when a change-point model is fitted to data described by a smooth curve, the rate of convergence slows down to and the limit distribution changes to that of the minimizer of a continuous Gaussian process. In this paper we provide a bridge between these two extreme scenarios by studying the limit behavior of change-point estimates under varying degrees of model mis-specification by smooth curves, which can be viewed as local alternatives. We find that the limiting regime depends on how quickly the alternatives approach a change-point model. We unravel a family of 'intermediate' limits that can transition, at least qualitatively, to the limits in the two extreme scenarios. The theoretical results are illustrated via a set of carefully designed simulations. We also demonstrate how inference for the change-point parameter can be performed in absence of knowledge of the underlying scenario by resorting to subsampling techniques that involve estimation of the convergence rate. |
DOI | 10.1214/15-AOS1362 |
Alternate Journal | Ann Stat |
Original Publication | Asymptotics for change-point models under varying degrees of mis-specification. |
PubMed ID | 26681814 |
PubMed Central ID | PMC4678008 |
Grant List | P01 CA142538 / CA / NCI NIH HHS / United States |
ASYMPTOTICS FOR CHANGE-POINT MODELS UNDER VARYING DEGREES OF MIS-SPECIFICATION.
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