Date Available
5-23-2022
Year of Publication
2020
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
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)
Recommended Citation
Ren, Weihang, "MOMENT KERNELS FOR T-CENTRAL SUBSPACE" (2020). Theses and Dissertations--Statistics. 48.
https://uknowledge.uky.edu/statistics_etds/48
