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Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…
While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…
The famous G\"odel incompleteness theorem states that for every consistent sufficiently rich formal theory T there exist true statements that are unprovable in T. Such statements would be natural candidates for being added as axioms, but…
Providing guarantees on the safe operation of robots against edge cases is challenging as testing methods such as traditional Monte-Carlo require too many samples to provide reasonable statistics. Built upon recent advancements in…
Statistical procedures rarely retain all features of the observed data. A sufficient statistic removes information irrelevant to a parameter; a maximum likelihood estimate compresses an empirical objective into an optimizing point; and a…
This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and…
We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions. This…
This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…
Missing data is pervasive in econometric applications, and rarely is it plausible that the data are missing (completely) at random. This paper proposes a methodology for studying the robustness of results drawn from incomplete datasets.…
Minimum divergence methods are popular tools in a variety of statistical applications. We consider tubular model adequacy tests, and demonstrate that the new divergences that are generated in the process are very useful in robust…
Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…
Under what condition is a random constraint satisfaction problem hard to refute by the sum-of-squares (SoS) algorithm? A sufficient condition is t-wise uniformity, that is, each constraint has a t-wise uniform distribution of satisfying…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
Conformal prediction is a generic methodology for finite-sample valid distribution-free prediction. This technique has garnered a lot of attention in the literature partly because it can be applied with any machine learning algorithm that…
Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
Estimates based on 2x2 tables of frequencies are widely used in statistical applications. However, in many cases these tables are incomplete in the sense that the data required to compute the frequencies for a subset of the cells defining…
A histogram estimate of the Radon-Nikodym derivative of a probability measure with respect to a dominating measure is developed for binary sequences in $\{0,1\}^{\mathbb{N}}$. A necessary and sufficient condition for the consistency of the…