Date of Award


Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Statistics (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

David Hemmer

Committee Member 1

Iosif Pinelis

Committee Member 2

Qiuying Sha

Committee Member 3

Kui Zhang

Committee Member 4

Chee-Wooi Ten


This dissertation includes four Chapters. A brief description of each chapter is organized as follows.

In Chapter 1, some developments on multiple hypotheses tests are introduced. Some preliminaries about the definition and the assumption are included.

In Chapter 2, a Stable Combination Test is proposed to combine $p$-values from multiple hypotheses tests. We show the proposed method controls the family-wise error rate at the target level and maintains asymptotically optimal power even when the elementary p-values from the individual hypotheses are dependent.

In Chapter 3, a deeper dig into the additive p-value combination test is performed. A common idea behind some existing combination tests including the Stable Combination Test is extracted and a unified framework is proposed. The tails of the combined test statistics in this framework can be approximated by stable distribution. The tests in this framework are proven to have a well-controlled family-wise error rate and non-trivial power.

In Chapter 4, we illustrate the usefulness of the proposed unified framework by capturing the dynamic structure instabilities of Granger causality in a vector autoregression model. The p-value combination tests in the framework are easy to implement, robust to dependence, and have comparable performance to the bootstrap technique.