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Related papers: Higher-order approximate confidence intervals

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Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…

Statistics Theory · Mathematics 2010-03-16 Benedikt M. Pötscher , Ulrike Schneider

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…

Statistics Theory · Mathematics 2013-06-11 Xinjia Chen

Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical…

Statistics Theory · Mathematics 2021-01-19 Ji Xu , Arian Maleki , Kamiar Rahnama Rad , Daniel Hsu

In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…

Methodology · Statistics 2018-10-10 Richard Minkah , Tertius de Wet

Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can…

Statistics Theory · Mathematics 2024-03-15 Ian Waudby-Smith , David Arbour , Ritwik Sinha , Edward H. Kennedy , Aaditya Ramdas

We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $\theta$ that utilizes the uncertain prior information that a distinct scalar parameter…

Methodology · Statistics 2020-09-17 Paul Kabaila , Nishika Ranathunga

Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…

Numerical Analysis · Mathematics 2020-05-07 Zhijian He , Xiaoqun Wang

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

The goal of any estimation study is an interval estimation of a the parameter(s) of interest. These estimations are mostly expressed using empirical confidence intervals that are based on sample point estimates of the corresponding…

Methodology · Statistics 2018-07-03 Ilya Novikov

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

Machine Learning · Statistics 2014-02-21 Keisuke Yamazaki

We discuss a new way of constructing pointwise confidence intervals for the distribution function in the current status model. The confidence intervals are based on the smoothed maximum likelihood estimator (SMLE) and constructed using…

Statistics Theory · Mathematics 2017-03-27 Piet Groeneboom , Kim Hendrickx

We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic…

Probability · Mathematics 2012-12-12 Noufel Frikha , Stephane Menozzi

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…

Statistics Theory · Mathematics 2023-04-03 Luca Maestrini , Aishwarya Bhaskaran , Matt P. Wand

We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…

Computation · Statistics 2026-05-19 Jeong Eun Lee , Geoff K. Nicholls , Robin J. Ryder

The recent paper "Simple confidence intervals for MCMC without CLTs" by J.S. Rosenthal, showed the derivation of a simple MCMC confidence interval using only Chebyshev's inequality, not CLT. That result required certain assumptions about…

Statistics Theory · Mathematics 2021-07-01 Yu Hang Jiang , Tong Liu , Zhiya Lou , Jeffrey S. Rosenthal , Shanshan Shangguan , Fei Wang , Zixuan Wu

Objectives: Estimation of areas under receiver operating characteristic curves (AUCs) and their differences is a key task in diagnostic studies. We aimed to derive, evaluate, and implement simple sample size formulas for such studies with a…

Methodology · Statistics 2022-08-03 Di Shu , Guangyong Zou

For the quantification of QoE, subjects often provide individual rating scores on certain rating scales which are then aggregated into Mean Opinion Scores (MOS). From the observed sample data, the expected value is to be estimated. While…

Methodology · Statistics 2018-06-05 Tobias Hossfeld , Poul E. Heegaard , Martin Varela , Lea Skorin-Kapov

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…

Computation · Statistics 2024-04-04 Yves Deville

We derive a computationally convenient formula for the large sample coverage probability of a confidence interval for a scalar parameter of interest following a preliminary hypothesis test that a specified vector parameter takes a given…

Methodology · Statistics 2019-04-29 Paul Kabaila , Rupert E. H. Kuveke

Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of…

Methodology · Statistics 2016-12-28 Chaoyu Yu , Peter D. Hoff