Dimension Reduction for the Conditional Kth Moment via Central Solution Space

Open Access
Author:
Dong, Yuexiao
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 28, 2016
Committee Members:
  • Bing Li, Thesis Advisor
  • Runze Li, Thesis Advisor
Keywords:
  • dimension reduction space
  • central space
  • central solution space
  • central kth moment solution space
  • central kth moment space
Abstract:
The original aim of dimension reduction is to find linear combinations of predictor X, which contain all the regression information of Y versus X. Since the introduction of the very first dimension reduction methods such as OLS and SIR, various dimension reduction methods have been invented, such as SAVE and PHD. The invention of central mean subspace enriched the context of dimension reduction and brought more insight into existing dimension reduction methods. This idea is expanded later to central kth moment space. However, those methods all require stringent conditions on the joint distribution of the predictor. In this thesis, via the notion of central solution space, we want to relax the elliptical distribution assumption required by central kth moment space estimators. Central kth moment solution space is introduced and its estimators are compared with existing methods by simulation.