Related papers: Nearly Optimal Robust Mean Estimation via Empirica…
In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
In this paper, we explore the asymptotically optimal tuning parameter choice in ridge regression for estimating nuisance functions of a statistical functional that has recently gained prominence in conditional independence testing and…
A general non-Gaussian semiparametric model is adopted to characterize the measurement vectors, i.e.\ the \textit{snapshots}, collected by a linear array. Moreover, the recently derived \textit{robust semiparametric efficient} $R$-estimator…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that…
Consider the problem of simultaneous estimation of location and variance matrix under Huber's contaminated Gaussian model. First, we study minimum $f$-divergence estimation at the population level, corresponding to a generative adversarial…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the…
Robust mean estimation is one of the most important problems in statistics: given a set of samples in $\mathbb{R}^d$ where an $\alpha$ fraction are drawn from some distribution $D$ and the rest are adversarially corrupted, we aim to…
Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Most of the modern literature on robust mean estimation focuses on designing estimators which obtain optimal sub-Gaussian concentration bounds under minimal moment assumptions and sometimes also assuming contamination. This work looks at…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…
We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…