Related papers: On approximate robust confidence distributions

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…

The focus of this paper is on the quantification of sampling variation in frequentist probabilistic forecasts. We propose a method of constructing confidence sets that respects the functional nature of the forecast distribution, and use…

Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…

It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof does not rely on existence of invariant measures, and…

We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to…

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…

The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…

We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…

Based on the median and the median absolute deviation estimators, and the Hodges-Lehmann and Shamos estimators, robustified analogues of the conventional $t$-test statistic are proposed. The asymptotic distributions of these statistics are…

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…

We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…

The minimum divergence estimators have proved to be useful tools in the area of robust inference. The robustness of such estimators are measured using the classical Influence functions. However, in many complex situations like testing a…

In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…

We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…

Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…

We congratulate the authors on their exciting paper, which introduces a novel idea for assessing the estimation bias in causal estimates. Doubly robust estimators are now part of the standard set of tools in causal inference, but a typical…