Statistical methods for binomial and Gaussian sequences

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Biscarri, William

Contributors dc:contributor

• Zhao, Sihai Dave
• Brunner, Robert
• Zhu, Ruoqing
• Chen, Yuguo

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

Statement dc:rights

• Copyright 2019 William Dionis Biscarri

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106468