Year of Publication

2020

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Xiangrong Yin

Abstract

The T-central subspace allows one to perform sufficient dimension reduction for any statistical functional of interest. We propose a general estimator using a third moment kernel to estimate the T-central subspace. In particular, in this dissertation we develop sufficient dimension reduction methods for the central mean subspace via the regression mean function and central subspace via Fourier transform, central quantile subspace via quantile estimator and central expectile subsapce via expectile estima- tor. Theoretical results are established and simulation studies show the advantages of our proposed methods.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2020.252

Funding Information

This dissertation is supported in part by National Science Foundation grant CIF- 1813330. (01/2019 - 05/2019)

Available for download on Monday, May 23, 2022

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