Browsing Statistics by Title
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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 ... 
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 ... 
ShapeConstrained Inference for ConcaveTransformed Densities and their Modes
(20131114)We consider inference about functions estimated via shape constraints based on concavity. We consider logconcave densities and other “concavetransformed” densities on the real line, where a concavetransformed class is ... 
SpaceTime Smoothing Models for Surveillance and Complex Survey Data
Area and timespecific estimates of disease rates, causespecific mortality rates and other key health indicators are of great interest for health care and policy purposes. Such estimates provide the information needed to ... 
Statistical Hurdle Models for Single Cell Gene Expression: Differential Expression and Graphical Modeling
This dissertation describes a set of statistical methods developed for analysis of single cell gene expression. A characteristic of single cell expression is bimodal expression, in which two clusters of expression are ... 
Statistical inference using Kronecker structured covariance
(20131114)We present results for testing and estimation in the context of separable covariance models. We concentrate on two types of data: relational data and crossclassified data. Relational data is frequently represented by a ... 
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 ... 
Testing Independence in High Dimensions & Identifiability of Graphical Models
In this thesis two problems in multivariate statistics will be studied. In the first chaper, we treat the problem of testing independence between m continuous observations when m can be larger than the available sample ... 
Tests for Differences between Least Squares and Robust Regression Parameter Estimates and Related Topics
(20130417)At the present time there is no well accepted test for comparing least squares and robust linear regression coefficient estimates. To fill this gap we propose and demonstrate the efficacy of two Waldlike statistical tests ... 
Theory and Methods for Tensor Data
We present novel methods and new theory in the statistical analysis of tensorvalued data. A tensor is a multidimensional array. When data come in the form of a tensor, special methods and models are required to capture ... 
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 ... 
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 ... 
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 ... 
The weighted likelihood bootstrap and an algorithm for prepivoting
(1991)The method of bootstrapping, which has transformed the theory and practice of frequentist statistical inference, is applicable within the Bayesian paradigm. Rather than simulating data that might have been observed, this ...