##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Claudia Kirch

#### Technical University Kaiserslautern

## Resampling Methods in Change-Point Analysis

##### Abstract:

Change-point analysis deals with the question whether an observed stochastic process follows one model or whether the underlying model changes at least once during the observational period. In change-point analysis critical values for testing procedures are usually obtained by distributional asymptotics. However, convergence is often rather slow. Moreover, these critical values do not sufficiently reflect possible dependency. Using resampling methods one can often obtain better approximations, especially for small sample sizes or dependent data. Similarly one can obtain confidence intervals of the change-point using resampling methods, which are often better than asymptotic confidence intervals. Recently sequential change-point analysis has become more and more popular. In this setup, one gets the observations `online', i.e. sequentially one-by-one, after having observed a historic data set without change. For each new observation one checks whether one can still assume the null hypothesis. This is becoming more and more important in such diverse fields as medicine, material science or finance. In such a setting we can make use of the new incoming observations for the bootstrap. From a practical point of view this is computationally expensive, so one can think of alternatives which are cheaper but still very good. From a theoretical point of view this means that we have new critical values with each incoming observation, so the question is whether this procedure remains consistent. In this talk we focus on theoretically examining different bootstrap procedures for change-point tests and comparing them in a simulation study.

Host: Dimitris Politis

### January 18, 2008

### 11:00 AM

### AP&M 6402

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