Author ORCID Identifier

https://orcid.org/0000-0002-2835-3276

Year of Publication

2017

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Xiangrong Yin

Abstract

We introduce a new class of measures for testing independence between two random vectors, which uses expected difference of conditional and marginal characteristic functions. By choosing a particular weight function in the class, we propose a new index for measuring independence and study its property. Two empirical versions are developed, their properties, asymptotics, connection with existing measures and applications are discussed. Implementation and Monte Carlo results are also presented.

We propose a two-stage sufficient variable selections method based on the new index to deal with large p small n data. The method does not require model specification and especially focuses on categorical response. Our approach always improves other typical screening approaches which only use marginal relation. Numerical studies are provided to demonstrate the advantages of the method.

We introduce a novel approach to sufficient dimension reduction problems using the new measure. The proposed method requires very mild conditions on the predictors, estimates the central subspace effectively and is especially useful when response is categorical. It keeps the model-free advantage without estimating link function. Under regularity conditions, root-n consistency and asymptotic normality are established. The proposed method is very competitive and robust comparing to existing dimension reduction methods through simulations results.

Digital Object Identifier (DOI)

https://doi.org/10.13023/ETD.2017.255

Available for download on Wednesday, July 11, 2018

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