Related papers: On the length of post-model-selection confidence i…

In this paper we develop procedures to construct simultaneous confidence bands for $\tilde p$ potentially infinite-dimensional parameters after model selection for general moment condition models where $\tilde p$ is potentially much larger…

While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the…

The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the most famous of these attempts. We argue that, despite its…

Introduction: estimation of confidence intervals (CIs) of binomial proportions has been reviewed more than once but the directional interpretation, distinguishing the overestimation from the underestimation, was neglected while the sample…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…

A reliable representation of uncertainty is essential for the application of modern machine learning methods in safety-critical settings. In this regard, the use of credal sets (i.e., convex sets of probability distributions) has recently…

Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an…

Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…

This paper reviews two main types of prediction interval methods under a parametric framework. First, we describe methods based on an (approximate) pivotal quantity. Examples include the plug-in, pivotal, and calibration methods. Then we…

This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…

Interval identification of parameters such as average treatment effects, average partial effects and welfare is particularly common when using observational data and experimental data with imperfect compliance due to the endogeneity of…

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…

A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…

Bootstrap is a widely used technique that allows estimating the properties of a given estimator, such as its bias and standard error. In this paper, we evaluate and compare five bootstrap-based methods for making confidence intervals: two…

The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of…

This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many…

We propose a test of the significance of a variable appearing on the Lasso path and use it in a procedure for selecting one of the models of the Lasso path, controlling the Family-Wise Error Rate. Our null hypothesis depends on a set A of…

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…