Related papers: Confidence Intervals from One One Observation
Conformal prediction delivers prediction intervals with distribution-free coverage, but its intervals can look overconfident in regions where the model is extrapolating, because standard conformal scores do not explicitly represent…
This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable.…
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in…
Reliable application of machine learning is of primary importance to the practical deployment of deep learning methods. A fundamental challenge is that models are often unreliable due to overconfidence. In this paper, we estimate a model's…
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…
Confidence intervals are an established means of portraying uncertainty about an inferred parameter and can be generated through the use of confidence distributions. For a confidence distribution to be ideal, it must maintain frequentist…
In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…
We propose a new method called localized conformal prediction, where we can perform conformal inference using only a local region around a new test sample to construct its confidence interval. Localized conformal inference is a natural…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
The length-biased Birnbaum-Saunders distribution is both useful and practical for environmental sciences. In this paper, we initially derive some new properties for the length-biased Birnbaum-Saunders distribution, showing that one of its…
We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…
The Clopper-Pearson confidence interval has ever been documented as an exact approach in some statistics literature. More recently, such approach of interval estimation has been introduced to probabilistic control theory and has been…
This article presents methods for the construction of two-sided and one-sided simultaneous hyperbolic bands for the logistic and probit regression models when the predictor variable is restricted to a given interval. The bands are…
We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this paper, we assess the performance of four common proportion interval estimators: the Wald,…
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…
It is well known that it is impossible to construct useful confidence intervals (CIs) about the mean or median of a response $Y$ conditional on features $X = x$ without making strong assumptions about the joint distribution of $X$ and $Y$.…
Estimating the difference between two binomial proportions will be investigated, where Bayesian, frequentist and fiducial (BFF) methods will be considered. Three vague priors will be used, the Jeffreys prior, a divergence prior and the…