TitleImputation of automatic control algorithms and estimation in high-dimensional linear regression
NameYe, Fei (author), Zhang, Cun-Hui (chair), Zhang, Tong (internal member), Shepp, Lawrence (internal member), Chaovalitwongse, Wanpracha (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectStatistics and Biostatistics,
DescriptionThis 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.
NoteIncludes bibliographical references (p. 58-59)
Noteby Fei Ye
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.