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Hypothesis Tests for High-Dimensiona...

University of Toronto (Canada)., Statistics.

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Hypothesis Tests for High-Dimensional Functional Data /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hypothesis Tests for High-Dimensional Functional Data // David Colin Decker.
Author:	Decker, David Colin,
Description:	1 electronic resource (155 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-05, Section: B.
Contained By:	Dissertations Abstracts International86-05B.
Subject:	Statistics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31483083
ISBN:	9798342750882

Hypothesis Tests for High-Dimensional Functional Data /
Decker, David Colin,

Hypothesis Tests for High-Dimensional Functional Data /David Colin Decker. - 1 electronic resource (155 pages)

Source: Dissertations Abstracts International, Volume: 86-05, Section: B.

High-dimensional functional data have the feature that each observational unit consists of many functional recordings. Such data are commonly generated by modern medical devices. Examples include medical imaging devices (for example fMRI and EEG devices), high through-put time-course gene sequencing devices, and high through-put devices that measure time-course microbiome composition. In the case of fMRI studies of brain activity, a time-series is recorded discretely at around 100 sites corresponding to electrodes placed on the scalp of each participant.In both the paired two-sample and independent two-sample settings we develop two-sample tests of equality of many functional means. We use a novel mixed-norm test statistic and develop a Gaussian multiplier bootstrap procedure to estimate the quantile of the test statistic under the null hypothesis of equality of overall mean. Our tests are shown theoretically to be accurate and powerful even when the number of functional recordings per observation is much larger than the sample size.Our procedure allows us to control the family-wise error incurred by testing many simultaneous functional hypotheses without conservative multiple testing corrections, and makes no assumption at all on the dependence structure across the functional recordings within each observation.In addition to proving theoretical guarantees related to the power and level of our test, we show that our test compares favorably to current state of the art tests by way of a simulation study and the analysis two `real world' data sets generated by an EEG and fMRI study.

English

ISBN: 9798342750882Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Medical imaging devices

Hypothesis Tests for High-Dimensional Functional Data /
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520 $a High-dimensional functional data have the feature that each observational unit consists of many functional recordings. Such data are commonly generated by modern medical devices. Examples include medical imaging devices (for example fMRI and EEG devices), high through-put time-course gene sequencing devices, and high through-put devices that measure time-course microbiome composition. In the case of fMRI studies of brain activity, a time-series is recorded discretely at around 100 sites corresponding to electrodes placed on the scalp of each participant.In both the paired two-sample and independent two-sample settings we develop two-sample tests of equality of many functional means. We use a novel mixed-norm test statistic and develop a Gaussian multiplier bootstrap procedure to estimate the quantile of the test statistic under the null hypothesis of equality of overall mean. Our tests are shown theoretically to be accurate and powerful even when the number of functional recordings per observation is much larger than the sample size.Our procedure allows us to control the family-wise error incurred by testing many simultaneous functional hypotheses without conservative multiple testing corrections, and makes no assumption at all on the dependence structure across the functional recordings within each observation.In addition to proving theoretical guarantees related to the power and level of our test, we show that our test compares favorably to current state of the art tests by way of a simulation study and the analysis two `real world' data sets generated by an EEG and fMRI study.
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