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Methods and Theory for Nonparametric Inference in High-Dimensional Settings.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Methods and Theory for Nonparametric Inference in High-Dimensional Settings./
作者:	Xiang, Yunhua.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	147 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
標題:	Biostatistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28547011
ISBN:	9798535507071

Methods and Theory for Nonparametric Inference in High-Dimensional Settings.
Xiang, Yunhua.

Methods and Theory for Nonparametric Inference in High-Dimensional Settings. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 147 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--University of Washington, 2021.

This item must not be sold to any third party vendors.

This dissertation addresses nonparametric estimation and inference problems of graphical modeling, linear association assessment, and matrix completion. First, we introduce a flexible framework for nonparametric graphical modeling. We propose three nonparametric measures of conditional dependence, which have theoretically optimal estimators that allow incorporation of flexible machine learning techniques and yield wald-type confidence intervals. In the second project, we propose a nonparametric parameter to measure the linear association between the outcome and explanatory variables. This parameter is always explicitly defined even when the true relationship is nonlinear and is equivalent with the regression coefficient under a linear model space. Thus, its estimator can be a more robust alternative to the standard model-based techniques to estimate the coefficients of a linear model. In the final project, we theoretically show that nuclear-norm penalization used for recovering low-rank matrices, remains effective even when the underlying matrices are generated by a low-dimensional non-linear manifold. The convergence rate can be expressed as a function of the size of the matrix, as well as the smoothness and dimension of the manifold, which is minimax optimal (up to a log term).

ISBN: 9798535507071Subjects--Topical Terms:

1002712
Biostatistics.
Subjects--Index Terms:

Graphical modeling

Methods and Theory for Nonparametric Inference in High-Dimensional Settings.
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520 $a This dissertation addresses nonparametric estimation and inference problems of graphical modeling, linear association assessment, and matrix completion. First, we introduce a flexible framework for nonparametric graphical modeling. We propose three nonparametric measures of conditional dependence, which have theoretically optimal estimators that allow incorporation of flexible machine learning techniques and yield wald-type confidence intervals. In the second project, we propose a nonparametric parameter to measure the linear association between the outcome and explanatory variables. This parameter is always explicitly defined even when the true relationship is nonlinear and is equivalent with the regression coefficient under a linear model space. Thus, its estimator can be a more robust alternative to the standard model-based techniques to estimate the coefficients of a linear model. In the final project, we theoretically show that nuclear-norm penalization used for recovering low-rank matrices, remains effective even when the underlying matrices are generated by a low-dimensional non-linear manifold. The convergence rate can be expressed as a function of the size of the matrix, as well as the smoothness and dimension of the manifold, which is minimax optimal (up to a log term).
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