##### Department of Mathematics,

University of California San Diego

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### Statistics

## Yajun Mei

#### CalTech

## Change Point Problems for Composite Pre-Change Distribution

##### Abstract:

Potential Statistics Recruitment CandidateChange point problems have a variety of applications including industrial quality control, reliability, clinical trials, surveillance, and security systems. By monitoring data streams which are generated from the process, we are interested in quickly detecting malfunctioning once the process goes out of control, while keeping false alarms as infrequent as possible when the process is in control. Suppose that $f_ heta(x)$, the distribution of the data, is indexed by $ heta$, a vector of one or more parameters. Most research has been done under the assumption that the value of $ heta$ is known before a change occurs. In this talk, we investigate the situation where the value of $ heta$ is composite before a change occurs. We present a new formulation of the problem by specifying required average time to detect after the value of $ heta$ shifts to a specified $ heta_1$ and trying to minimize the frequency of false alarms over a range of possible value $ heta$ before a change occurs. Asymptotically optimal procedures will be presented.

Host: Ian Abramson

### February 6, 2003

### 4:00 PM

### AP&M 6438

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