Related papers: High-Confident Nonparametric Fixed-Width Uncertain…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

We consider independent random variables (r.v.'s) with a common mean $\mu$ that either satisfy Lindeberg's condition, or are symmetric around $\mu$. Present forms of existing functional central limit theorems (FCLT's) for Studentized…

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

Prediction sets provide a means of quantifying the uncertainty in predictive tasks. Using held out calibration data, conformal prediction and risk control can produce prediction sets that exhibit statistically valid error control in a…

This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide…

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known…

Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…

High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve…

In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence…

Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We…

The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…

In this paper, we have established a unified framework of multistage parameter estimation. We demonstrate that a wide variety of statistical problems such as fixed-sample-size interval estimation, point estimation with error control,…

We argue that randomized controlled trials (RCTs) are special even among settings where average treatment effects are identified by a nonparametric unconfoundedness assumption. This claim follows from two results of Robins and Ritov (1997):…

Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional…

Conformal prediction provides prediction sets with coverage guarantees. The informativeness of conformal prediction depends on its efficiency, typically quantified by the expected size of the prediction set. Prior work on the efficiency of…

We study properties of confidence intervals (CIs) for the difference of two Bernoulli distributions' success parameters, $p_x - p_y$, in the case where the goal is to obtain a CI of a given half-width while minimizing sampling costs when…

When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…