Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been proposed for this task which make fewer assumptions on the distributions than traditional parametric approach. However, none of the existing kernel statistics has provided a computationally efficient way to characterize the extremal behavior ...

Using data from 17 years of a large and nationally representative panel study from Germany, the authors examined whether there is a set point for life satisfaction (LS)--stability across time, even though it can be perturbed for short periods by life events. The authors found that 24% of respondents changed significantly in LS from the first 5 years to the last 5 years and that stability declin...

The change-point problem is reformulated as a penalized likelihood estimation problem. A new non-convex penalty function is introduced to allow consistent estimation of the number of change points, and their locations and sizes. Penalized likelihood methods based on LASSO and SCAD penalties may not satisfy such a property. The asymptotic properties for the local solutions are established and nu...

ALEXANDER AUE0, LAJOS HORVÁTH1, MARIE HUŠKOVÁ2 AND PIOTR KOKOSZKA3 0Department of Mathematical Sciences, Clemson University, O-324 Martin Hall, Clemson, SC 29634, USA E-mail: [email protected] 1Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, UT 84112–0090, USA E-mails: [email protected] and [email protected] 2Department of Statistics, Charles University...

A method for efficiently calculating exact marginal, conditional and joint distributions for change points defined by general finite state Hidden Markov Models is proposed. The distributions are not subject to any approximation or sampling error once parameters of the model have been estimated. It is shown that, in contrast to sampling methods, very little computation is needed. The method prov...

This paper discusses Bayesian inference in change-point models. Existing approaches involve placing a (possibly hierarchical) prior over a known number of change-points. We show how two popular priors have some potentially undesirable properties (e.g. allocating excessive prior weight to change-points near the end of the sample) and discuss how these properties relate to imposing a fixed number...

The contribution presents to analyses and comparison of the recursive (sliding window) Bayesian autoregressive normalized change-point detector (RBACDN) and the reversible jump Markov chain Monte Carlo method (RJMCMC) when they are used for the localization of signal changes (change-point detection). The choice of priors and parameter setting for the RJMCMC and the RBACDN are discussed. The eva...

Reconstruction of a bilevel function such as a bar code signal in a partially blind deconvolution problem is an important task in industrial processes. Existing methods are based on either the local approach or the regularization approach with a total variation penalty. This article reformulated the problem explicitly in terms of change points of the 0-1 step function. The bilevel function is t...

We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures. The results demonstrate that the best achievable rates of conv...

Change points and changing regimes can be observed in many statistical time series. In this paper we analyze the most influential approaches of modeling these occurrences. Along with the theory some of the most interesting applications are presented. We find out that use of terminology is not unique, leading to considerable differences between the models, as will be pointed out.