This thesis develops flexible and principled nonparametric learning algorithms to explore, understand, and predict high dimensional and complex datasets. Such data appear frequently in modern scientific domains and lead to numerous important applications. For example, exploring high dimensional functional magnetic resonance imaging data helps us to better understand brain functionalities; infer...

The literature on statistical test of stochastic dominance has thus far been concerned with univariate distributions. This paper presents nonparametric statistical tests for multivariate distributions. This allows a nonparametric treatment of multiple welfare indicators. These test are applied to a time series of cross-section datasets on household level total expenditure and non labour market ...

A wide variety of tools are available, both parametric and nonparametric, for analyzing spatial data. However, it is not always clear how to translate statistical inferences into decision recommendations. This article explores the possibilities of estimating the effects of decision options using very direct manipulation of data, bypassing formal statistical analysis. We illustrate with the appl...

The varying-coefficient model is an important class of nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is large, the issue of variable selection arises. In this paper, we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra-high dimensional varying-...

A statistical analysis of the nucleotide sequence variability in 14 published hepatitis B virus (HBV) genomes was carried out using parametric and nonparametric methods. A parametric statistical model revealed that the different regions of the genome differed significantly in their variability. The conclusion was supported by a nonparametric kernel-density model of the HBV genome. Genes S, C, a...

Nonparametric models are versatile, albeit computationally expensive, tool for modeling mixture models. In this paper, we introduce spectral methods for the two most popular nonparametric models: the Indian Buffet Process (IBP) and the Hierarchical Dirichlet Process (HDP). We show that using spectral methods for the inference of nonparametric models are computationally and statistically efficie...

• In the independent two-sample t-test, we assume normality, independence, and equal variances. • This t-test is robust against nonnormality, but is sensitive to dependence. • If n1 is close to n2, then the test is moderately robust against unequal variance (σ 1 6= σ 2). But if n1 and n2 are quite different (e.g. differ by a ratio of 3 or more), then the test is much less robust. • How to deter...