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We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the…

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…

Robust tests of general composite hypothesis under non-identically distributed observations is always a challenge. Ghosh and Basu (2018, Statistica Sinica, 28, 1133--1155) have proposed a new class of test statistics for such problems based…

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…

This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…

Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering…

How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…

Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…

The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that…

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…

Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With…

Robust causal discovery from observational data under imperfect prior knowledge remains a significant and largely unresolved challenge. Existing methods typically presuppose perfect priors or can only handle specific, pre-identified error…

This paper is concerned with inference in the linear model with dyadic data. Dyadic data is data that is indexed by pairs of "units", for example trade data between pairs of countries. Because of the potential for observations with a unit…

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…

Effective machine learning models can automatically learn useful information from a large quantity of data and provide decisions in a high accuracy. These models may, however, lead to unfair predictions in certain sense among the population…

Statistical modeling is often used to measure the strength of evidence for or against hypotheses on given data. We have previously proposed an information-dynamic framework in support of a properly calibrated measurement scale for…