Statistical methods for binomial and Gaussian sequences

Biscarri, William

Permalink

https://hdl.handle.net/2142/106468 Copy

Description

Title

Statistical methods for binomial and Gaussian sequences

Author(s)

Biscarri, William

Issue Date

2019-12-03

Director of Research (if dissertation) or Advisor (if thesis)

• Zhao, Sihai Dave
• Brunner, Robert

Doctoral Committee Chair(s)

• Zhao, Sihai Dave
• Brunner, Robert

Committee Member(s)

• Zhu, Ruoqing
• Chen, Yuguo

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• James Stein
• Poisson Binomial
• Random Forest
• Compound Decision Theory
• Empirical Bayes
• Community Detection

Abstract

We propose new methods and frameworks for approaching three different statistical sequence problems. The first is a tree-based computational method for calculating the Poisson Binomial distribution function, which is the distribution of a sum of independent but not identically distributed Bernoulli random variables. Our proposed scheme is shown to be the fastest available method for exact computation of the distribution function. The second problem we study is community detection and link probability estimation in network data. We propose a novel Random Forest methodology adapted to network data in order to approach these problems, which utilizes the Random Forest to construct a kernel encoding similarities between network vertices. To our knowledge, this is the first instance in which Random Forests have been applied to these problems. Unlike standard Random Forest approaches, these methods are fully unsupervised. The efficacy of the proposed methods is demonstrated via extensive simulations, and they are shown to achieve state of the art performance. Finally, we present a new approach for tackling the classical Normal means sequence problem, which takes a modeling perspective. This new perspective allows for the straightforward development of new estimators, which unlike most currently available estimators, are able to incorporate covariate information. Due to the perspective we take, we are further able to perform inference on parameters in the model. We provide several theoretical results that show our approach yields estimators with favorable properties. We also demonstrate the effectiveness of the proposed approach through a comprehensive simulation study.

Graduation Semester

2019-12

Type of Resource

text

Permalink

http://hdl.handle.net/2142/106468

Copyright and License Information

Copyright 2019 William Dionis Biscarri

Owning Collections