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Imputation of automatic control algorithms and estimation in high-dimensional linear regression
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Title
Imputation of automatic control algorithms and estimation in high-dimensional linear regression
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ETD_2290
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000052167
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eng
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theses
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Topic
Statistics and Biostatistics
Subject
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Topic
Automatic control
Subject
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(authority = ETD-LCSH)
Topic
Regression analysis
Abstract
This thesis contains two parts. In the first part, we study a semiparametric imputation method to simulate a time series of blood glucose level under certain closed-loop control algorithm of a diabetic patient equipped with a continuous glucose monitor and an insulin pump, from the "frozen" measurements under self-adjusted open-loop control. The Star One data set provided by Medtronic Inc illustrates the feasibility of a simple PID algorithm, as an example of automatic control algorithms, in controlling blood glucose levels from the perspective of reducing the A1c level and controlling hypoglycemia risk.
In the second part, we consider L1-penalized selection of variables and estimation of regression coefficients in a high-dimensional linear model. Under an L0 sparsity condition on the regression coefficients, we sharpen an upper bound of Candes and Tao (2007) for the L2 loss of the Dantzig selector and extend it to the Lq loss and the Lasso. By allowing q equals infinity, our bound implies the variable selection consistency of threshold Dantzig selectors. For the estimation of regression coefficients in Lr balls, we provide minimax lower bounds for the Lq risk and the tail quantiles of the Lq loss as well as sufficient conditions on the design matrix and penalty level for the Dantzig and Lasso estimators to attain these minimax rates.
In the second part, we consider L1-penalized selection of variables and estimation of regression coefficients in a high-dimensional linear model. Under an L0 sparsity condition on the regression coefficients, we sharpen an upper bound of Candes and Tao (2007) for the L2 loss of the Dantzig selector and extend it to the Lq loss and the Lasso. By allowing q equals infinity, our bound implies the variable selection consistency of threshold Dantzig selectors. For the estimation of regression coefficients in Lr balls, we provide minimax lower bounds for the Lq risk and the tail quantiles of the Lq loss as well as sufficient conditions on the design matrix and penalty level for the Dantzig and Lasso estimators to attain these minimax rates.
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electronic resource
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ix, 60 p. : ill.
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Ph.D.
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Includes bibliographical references (p. 58-59)
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by Fei Ye
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Ye
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Fei
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1983-
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Fei Ye
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Zhang
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Cun-Hui
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chair
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Advisory Committee
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Cun-Hui Zhang
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Zhang
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Tong
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internal member
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Advisory Committee
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Tong Zhang
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Shepp
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Lawrence
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internal member
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Lawrence Shepp
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Chaovalitwongse
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Wanpracha
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outside member
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Wanpracha Art Chaovalitwongse
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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2010
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2010-01
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xx
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Rutgers University Electronic Theses and Dissertations
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ETD
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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Identifier
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doi:10.7282/T3SB45WX
Genre
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ETD doctoral
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Rights
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The author owns the copyright to this work.
Copyright
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Copyright protected
Notice
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Availability
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Open
Reason
Permission or license
Note
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Ye
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Fei
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2009-12-10 17:51:33
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Fei Ye
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Rutgers University. Graduate School - New Brunswick
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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