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It's well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It's of the form$% | f(x)-s(x)| \leq (Cd)^{\frac{c}{d}}\left\Vert f\right\Vert_{h}$ where $C,c$ are constants, $h$ is the…

Numerical Analysis · Mathematics 2007-05-23 Lin-Tian Luh

We consider a linear regression model with regression parameter beta=(beta_1,...,beta_p) and independent and identically N(0,sigma^2) distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…

Methodology · Statistics 2017-10-18 Paul Kabaila , Khageswor Giri

We study the bootstrap for the maxima of the sums of independent random variables, a problem of high relevance to many applications in modern statistics. Since the consistency of bootstrap was justified by Gaussian approximation in…

Statistics Theory · Mathematics 2020-08-03 Hang Deng

This paper presents two results concerning uniform confidence intervals for the tail index and the extreme quantile. First, we show that it is impossible to construct a length-optimal confidence interval satisfying the correct uniform…

Statistics Theory · Mathematics 2022-10-25 Yuya Sasaki , Yulong Wang

In econometrics, many parameters of interest can be written as ratios of expectations. The main approach to construct confidence intervals for such parameters is the delta method. However, this asymptotic procedure yields intervals that may…

Statistics Theory · Mathematics 2019-04-16 Alexis Derumigny , Lucas Girard , Yannick Guyonvarch

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…

Information Theory · Computer Science 2021-11-29 Sebastian Espinosa , Jorge F. Silva , Pablo Piantanida

We consider a linear regression model with regression parameter beta =(beta_1, ..., beta_p) and independent and identically N(0, sigma^2)distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified…

Computation · Statistics 2009-04-17 Paul Kabaila , Khageswor Giri

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…

Statistics Theory · Mathematics 2012-12-21 Eric Marchand , William E. Strawderman

The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…

Statistics Theory · Mathematics 2012-02-24 Marc Hoffmann , Richard Nickl

Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Rajendran Raja

We consider the confidence interval centered on a frequentist model averaged estimator that was proposed by Buckland, Burnham & Augustin (1997). In the context of a simple testbed situation involving two linear regression models, we derive…

Methodology · Statistics 2023-06-29 Paul Kabaila , Alan H. Welsh , Christeen Wijethunga

This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B…

Information Theory · Computer Science 2015-10-13 Sudarshan Guruacharya , Hina Tabassum , Ekram Hossain

We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…

Data Analysis, Statistics and Probability · Physics 2020-05-27 A. D. Morozov , A. V. Lokhov , F. V. Tkachov

We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…

The asymptotic behaviour of the commonly used bootstrap percentile confidence interval is investigated when the parameters are subject to linear inequality constraints. We concentrate on the important one- and two-sample problems with data…

Statistics Theory · Mathematics 2022-12-06 Chunlin Wang , Paul Marriott , Pengfei Li

We evaluate the model averaged profile likelihood confidence intervals proposed by Fletcher and Turek (2011) in a simple situation in which there are two linear regression models over which we average. We obtain exact expressions for the…

Methodology · Statistics 2017-10-18 Paul Kabaila , A. H. Welsh , Waruni Abeysekera

Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…

Machine Learning · Statistics 2026-03-24 Wanrong Zhu , Zhipeng Lou , Ziyang Wei , Wei Biao Wu

We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…

Data Analysis, Statistics and Probability · Physics 2018-12-26 Igor Volobouev , A. Alexandre Trindade

This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and…

Statistics Theory · Mathematics 2025-01-22 Rajendranath Mondal , Aditi Kar Gangopadhyay , Raju Bhakta , Kousik Maiti

For the usual normal approximations to binomial, hypergeometric, or Poisson interval probabilities, we collect some simple but then reasonably sharp error bounds. For the Clopper-Pearson~(1934) binomial confidence bounds, we present,…

Other Statistics · Statistics 2026-02-26 Lutz Mattner