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Change-Point Detection in Mean and Variance or Both.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Change-Point Detection in Mean and Variance or Both./
作者:	Zhu, Zhen.
面頁冊數:	1 online resource (89 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-04, Section: A.
Contained By:	Dissertations Abstracts International85-04A.
標題:	Skewness. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30645537click for full text (PQDT)
ISBN:	9798380485517

Change-Point Detection in Mean and Variance or Both.
Zhu, Zhen.

Change-Point Detection in Mean and Variance or Both. - 1 online resource (89 pages)

Source: Dissertations Abstracts International, Volume: 85-04, Section: A.

Thesis (Ph.D.)--Stanford University, 2023.

Includes bibliographical references

The focus of this thesis is on developing statistical methods to identify change-points in datasets where there may be changes in both mean and variance. We propose novel statistical methods for detecting such change-points and discuss both type-I error approximations and power evaluations.Our first set of tests is based on score statistics for the single change-point problems and introduces a hyper-parameter to allow flexibility between change in the mean parameter and change in the variance parameter. We also introduce both box-type and ellipse-type statistics based on different shapes of the rejection region. Analyzing the score-based statistics is challenging due to the heavier than normal tails in the x2distribution in the variance component of the statistics. We develop theoretical methods that deal with this difficulty when approximating type-I error. Additionally, we provide marginal power calculations for assessing the effectiveness of these tests. The required modifications for both type-I error approximations and marginal power calculations for the interval change problems are discussed as well.Next, we propose tests based on the full generalized likelihood statistics and the box-type and ellipse-type statistics with the same hyper-parameter as in the score case. The theoretical results for this set of tests are simpler than the score tests because now both mean and variance components of our statistics are approximately Gaussian distributed. We provide type-I error approximations and marginal power calculations for the full generalized likelihood statistics in both single change-point and the interval change problems.Finally, we compare the power of all these statistics with the power of the classical change-point statistics which only allow change in the mean and assume variance is constant. We also examine some real-world datasets to demonstrate the effectiveness and pitfalls of these statistics.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798380485517Subjects--Topical Terms:

3698925
Skewness.
Index Terms--Genre/Form:

542853
Electronic books.

Change-Point Detection in Mean and Variance or Both.
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500 $a Source: Dissertations Abstracts International, Volume: 85-04, Section: A.
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504 $a Includes bibliographical references
520 $a The focus of this thesis is on developing statistical methods to identify change-points in datasets where there may be changes in both mean and variance. We propose novel statistical methods for detecting such change-points and discuss both type-I error approximations and power evaluations.Our first set of tests is based on score statistics for the single change-point problems and introduces a hyper-parameter to allow flexibility between change in the mean parameter and change in the variance parameter. We also introduce both box-type and ellipse-type statistics based on different shapes of the rejection region. Analyzing the score-based statistics is challenging due to the heavier than normal tails in the x2distribution in the variance component of the statistics. We develop theoretical methods that deal with this difficulty when approximating type-I error. Additionally, we provide marginal power calculations for assessing the effectiveness of these tests. The required modifications for both type-I error approximations and marginal power calculations for the interval change problems are discussed as well.Next, we propose tests based on the full generalized likelihood statistics and the box-type and ellipse-type statistics with the same hyper-parameter as in the score case. The theoretical results for this set of tests are simpler than the score tests because now both mean and variance components of our statistics are approximately Gaussian distributed. We provide type-I error approximations and marginal power calculations for the full generalized likelihood statistics in both single change-point and the interval change problems.Finally, we compare the power of all these statistics with the power of the classical change-point statistics which only allow change in the mean and assume variance is constant. We also examine some real-world datasets to demonstrate the effectiveness and pitfalls of these statistics.
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650 4 $a Epidemiology. $3 568544
650 4 $a Normal distribution. $3 3561025
650 4 $a Cholesterol. $3 3382101
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