Efficient estimation and order determination for sufficient dimension reduction

Open Access
Author:
Luo, Wei
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 22, 2014
Committee Members:
  • Bing Li, Dissertation Advisor
  • Bing Li, Committee Chair
  • Runze Li, Committee Member
  • Naomi S Altman, Committee Member
  • Jesse Louis Barlow, Committee Member
Keywords:
  • dimension reduction
  • order-determination
  • bootstrap
  • augmentation
  • semi-parametric
  • efficient estimation.
Abstract:
Sufficient dimension reduction (SDR) has driven intense interest in the recent decades as a solution to deal with high-dimensional data. The goal of SDR is to construct, usually by a linear transformation of the original predictor, a lower-dimensional sufficient statistic that serves as the new predictor in subsequent modeling. An important problem in SDR, is to determine the reduced dimension of the new predictor. In this dissertation, we first propose two order-determination methods that are applicable to a large class of SDR methods, with both of them proved consistent and shown efficient via simulation study and real data examples. Another part of the dissertation focuses on the development of a new class of efficient estimators of the linear transformation under various SDR assumptions, in a unifying semi-parametric approach. These estimators are expected to outperform their competitors in the literature, which were developed without consideration of semi-parametric efficiency. We derive the efficient score functions that generate these estimators, together with a computationally efficient algorithm. We also conduct the corresponding simulation studies and real data analysis to further show the effectiveness of the estimators in application.