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Methods for Handling Measurement Err...

Cai, Xiaochen.

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Methods for Handling Measurement Error and Sources of Variation in Functional Data Models.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Methods for Handling Measurement Error and Sources of Variation in Functional Data Models./
作者:	Cai, Xiaochen.
面頁冊數:	119 p.
附註:	Source: Dissertation Abstracts International, Volume: 76-04(E), Section: B.
Contained By:	Dissertation Abstracts International76-04B(E).
標題:	Biostatistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3665365
ISBN:	9781321377538

Methods for Handling Measurement Error and Sources of Variation in Functional Data Models.
Cai, Xiaochen.

Methods for Handling Measurement Error and Sources of Variation in Functional Data Models. - 119 p.

Source: Dissertation Abstracts International, Volume: 76-04(E), Section: B.

Thesis (Ph.D.)--Columbia University, 2015.

This item is not available from ProQuest Dissertations & Theses.

The overall theme of this thesis work concerns the problem of handling measurement error and sources of variation in functional data models. The first part introduces a wavelet-based sparse principal component analysis approach for characterizing the variability of multilevel functional data that are characterized by spatial heterogeneity and local features. The total covariance of the data can be decomposed into three hierarchical levels: between subjects, between sessions and measurement error. Sparse principal component analysis in the wavelet domain allows for reducing dimension and deriving main directions of random effects that may vary for each hierarchical level. The method is illustrated by application to data from a study of human vision. The second part considers the problem of scalar-on-function regression when the functional regressors are observed with measurement error. We develop a simulation-extrapolation method for scalar-on-function regression, which first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We introduce three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis. The third part discusses several extensions of the simulation-extrapolation method developed in the second part. Some of the extensions are illustrated by application to diffusion tensor imaging data.

ISBN: 9781321377538Subjects--Topical Terms:

1002712
Biostatistics.

Methods for Handling Measurement Error and Sources of Variation in Functional Data Models.
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502 $a Thesis (Ph.D.)--Columbia University, 2015.
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520 $a The overall theme of this thesis work concerns the problem of handling measurement error and sources of variation in functional data models. The first part introduces a wavelet-based sparse principal component analysis approach for characterizing the variability of multilevel functional data that are characterized by spatial heterogeneity and local features. The total covariance of the data can be decomposed into three hierarchical levels: between subjects, between sessions and measurement error. Sparse principal component analysis in the wavelet domain allows for reducing dimension and deriving main directions of random effects that may vary for each hierarchical level. The method is illustrated by application to data from a study of human vision. The second part considers the problem of scalar-on-function regression when the functional regressors are observed with measurement error. We develop a simulation-extrapolation method for scalar-on-function regression, which first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We introduce three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis. The third part discusses several extensions of the simulation-extrapolation method developed in the second part. Some of the extensions are illustrated by application to diffusion tensor imaging data.
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