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Statistical Methods for Manifold Recovery and C^{1, 1} Regression on Manifolds
Highdimensional data sets often have lowerdimensional structure taking the form of a submanifold of a Euclidean space. It is challenging but necessary to develop statistical methods for these data sets that respect the ... 
Topics in Statistics and Convex Geometry: Rounding, Sampling, and Interpolation
We consider a few aspects of the interplay between convex geometry and statistics. We consider three problems of interest: how to bring a convex body specified by a selfconcordant barrier into a suitably “rounded” position ... 
Preferential sampling and model checking in phylodynamic inference
Estimating population size fluctuations is one of the key tasks in Ecology. Traditional sampling based approaches to this task have limitations when populations of interest are extinct or are hard to reach, as is the case ... 
Topics on Least Squares Estimation
We revisit and make progress on some old but challenging problems concerning least squares estimation. Two major problems are addressed: (i) least squares estimation with heavytailed errors, and (ii) least squares estimation ... 
Discovering Interactions in Multivariate Time Series
In large collections of multivariate time series it is of interest to determine interactions between each pair of time series. Classically, interactions between time series have been studied using linear vector autoregressive ... 
Nonparametric inference on monotone functions, with applications to observational studies
In this dissertation, we study general strategies for constructing nonparametric monotone function estimators in two broad statistical settings. In the first setting, a sensible initial estimator of the monotone function ... 
ModelBased Penalized Regression
This thesis contains three chapters that consider penalized regression from a modelbased perspective, interpreting penalties as assumed prior distributions for unknown regression coefficients. In the first chapter, we ... 
Estimation and Testing Following Model Selection
The field of postselection inference focuses on developing solutions for problems in which a researcher uses a single dataset to both identify a promising set of hypotheses and conduct statistical inference. One promising ... 
Bayesian Methods for Graphical Models with Limited Data
Scientific studies in many fields involve understanding and characterizing dependence relationships among large numbers of variables. This can be challenging in settings where data is limited and noisy. Take survey data ... 
Parameter Identification and Assessment of Independence in Multivariate Statistical Modeling
We are interested in the extent to which, possibly causal, relationships can be statistically quantified from multivariate data obtained from a system of random variables. In the ideal setting, we would begin with refined ... 
Coevolution Regression and Composite Likelihood Estimation for Social Networks
We study how social networks and nodal attributes influence each other over time. A multiplicative coevolution regression (MCR) model is proposed for longitudinal network and nodal attribute data. The coevolution model is ... 
Linear Structural Equation Models with NonGaussian Errors: Estimation and Discovery
Linear structural equation models (SEMs) are multivariate models which encode direct causal effects. We focus on SEMs in which unobserved latent variables have been marginalized and only observed variables are explicitly ... 
Inference for HighDimensional Instrumental Variables Regression
This thesis concerns statistical inference for the components of a highdimensional regression parameter despite possible endogeneity of each regressor. Given a firststage linear model for the endogenous regressors and a ... 
Methods for estimation and inference for highdimensional models
This thesis tackles three different problems in highdimensional statistics. The first two parts of the thesis focus on estimation of sparse highdimensional undirected graphical models under nonstandard conditions, ... 
Topics in Graph Clustering
In this thesis, two problems in social networks will be studied. In the first part of the thesis, we focus on community recovery problems for social networks. There have been many recent theoretical advances in the modelbased ... 
Scalable Manifold Learning and Related Topics
The subject of manifold learning is vast and still largely unexplored. As a subset of unsupervised learning it has a fundamental challenge in adequately defining the problem but whose solution is to an increasingly important ... 
Applications of Robust Statistical Methods in Quantitative Finance
Financial asset returns and fundamental factor exposure data often contain outliers, observations that are inconsistent with the majority of the data. Both academic finance researchers and quantitative finance professionals ... 
Scalable Methods for the Inference of Identity by Descent
Identity by descent (IBD) describes the shared inheritance of DNA and underlies genetic similarity between individuals. Estimated IBD graphs describing the IBD relationships among individuals have many uses in statistical ... 
Projection and Estimation of International Migration
I propose techniques for improving both estimation and projection of international migration. By applying a Bayesian hierarchical modeling approach to net migration data, I produce projections of international migration ... 
Bayesian Methods for Inferring Gene Regulatory Networks
The recent explosion in the availability of gene expression data has opened up new possibilities in advancing our understanding of the fundamental processes of life. To keep up with the increasing size of the datasets, new ...