Lili Donovan

Senior Project Advisor

Kimihiro Noguchi, Ramadha Piyada Gamage

Document Type

Project

Publication Date

Spring 2022

Keywords

bootstrap, change point analysis, likelihood ratio test, nonparametric test

Abstract

Change point analysis is the process of determining changes to the mean of a sequence of independent observations. The goal is to determine the location of the change and how the change impacts the parameter in question. In this project, we applied the likelihood ratio test (LR) which uses a binary segmentation method to split the data at each change point. The data is iteratively split at each change point until every location of change is identified. The p-value is typically computed using the asymptotic distribution of the test statistic, however, it can be unreliable when the number of observations is too small. To improve our analysis of change points, we carried out a simulation study to analyze the empirical Type I error rate and the power of the LR test, using the parametric and nonparametric bootstrap. Under normal and exponential distributions it is found that the nonparametric bootstrap method makes the test reliable and robust for small, moderate, and large sample sizes. The improved bootstrap method is then applied to a real data set.

Department

Mathematics

Subjects - Topical (LCSH)

Bootstrap (Statistics)--Computer simulation

Genre/Form

essays

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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Included in

Mathematics Commons

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