Related papers: Asymptotically optimum estimation of a probability…

We present a complete framework for determining the asymptotic (or logarithmic) efficiency of estimators of large deviation probabilities and rate functions based on importance sampling. The framework relies on the idea that importance…

We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed…

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…

In nonparametric statistics an optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this classical point of view is subject to controversy as it requires to look for the worst behaviour…

The finite sample variance of an inverse propensity weighted estimator is derived in the case of discrete control variables with finite support. The obtained expressions generally corroborate widely-cited asymptotic theory showing that…

This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with…

This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…

Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…

In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

This work proposes a new loss function targeting classification problems, utilizing a source of information overlooked by cross entropy loss. First, we derive a series of the tightest upper and lower bounds for the probability of a random…

Importance sampling is a widely used technique to estimate properties of a distribution. This paper investigates trading-off some bias for variance by adaptively winsorizing the importance sampling estimator. The novel winsorizing…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…

Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…

Recently, it has been shown that incoherence is an unrealistic assumption for compressed sensing when applied to many inverse problems. Instead, the key property that permits efficient recovery in such problems is so-called local…

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

In experimental design, we are given a large collection of vectors, each with a hidden response value that we assume derives from an underlying linear model, and we wish to pick a small subset of the vectors such that querying the…