Related papers: Robust Statistical Estimators with Bounded Empiric…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…
The sharpest known high probability generalization bounds for uniformly stable algorithms (Feldman, Vondr\'{a}k, 2018, 2019), (Bousquet, Klochkov, Zhivotovskiy, 2020) contain a generally inevitable sampling error term of order…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a…
Sensitivity analysis is important to assess the impact of unmeasured confounding in causal inference from observational studies. The marginal sensitivity model (MSM) provides a useful approach in quantifying the influence of unmeasured…
Parameters defined via General Estimating Equations (GEE) can be estimated by maximizing the Empirical Likelihood (EL). Newey and Smith (2004) have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties,…
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…
We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the…
While there is a rich literature on robust methodologies for contamination in continuously distributed data, contamination in categorical data is largely overlooked. This is regrettable because many datasets are categorical and oftentimes…
Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find…
We introduce a new class of mean regression estimators -- penalized maximum tangent likelihood estimation -- for high-dimensional regression estimation and variable selection. We first explain the motivations for the key ingredient, maximum…
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions…
We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
This paper studies the robustness of estimated policy effects to changes in the distribution of covariates, a key determinant of the external validity of (quasi)-experimental results. I propose a novel robustness metric $\delta^*$ which…
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…