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The approximate Bernstein polynomial model, a mixture of beta distributions, is applied to obtain maximum likelihood estimates of the regression coefficients, and the baseline density and survival functions in an accelerated failure time…

Statistics Theory · Mathematics 2019-11-19 Zhong Guan

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…

Methodology · Statistics 2024-09-18 Isaac Gibbs , John J. Cherian , Emmanuel J. Candès

Standard conformal prediction offers a marginal guarantee on coverage, but for prediction sets to be truly useful, they should ideally ensure coverage conditional on each test point. Unfortunately, it is impossible to achieve exact,…

Machine Learning · Computer Science 2025-02-11 Jivat Neet Kaur , Michael I. Jordan , Ahmed Alaa

Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…

Machine Learning · Computer Science 2024-08-29 Harris Papadopoulos

We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…

Applications · Statistics 2020-07-07 Christian Bartels , Johanna Mielke , Ekkehard Glimm

Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…

Methodology · Statistics 2026-05-29 Aabesh Bhattacharyya , Boxuan Zhang , Rina Foygel Barber

Well-recommended methods of forming `confidence intervals' for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal…

Statistics Theory · Mathematics 2021-06-30 Paul H. Garthwaite , Maha W. Moustafa , Fadlalla G. Elfadaly

This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…

Optimization and Control · Mathematics 2024-08-27 Bo Rao , Liu Yang , Suhan Zhong , Guangming Zhou

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…

Statistics Theory · Mathematics 2026-05-22 Kenta Takatsu , Arun Kumar Kuchibhotla

A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…

Statistics Theory · Mathematics 2024-02-15 Weizhen Wang , Chongxiu Yu , Zhongzhan Zhang

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…

There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…

Information Theory · Computer Science 2017-09-26 Masato Kikuchi , Eiko Yamamoto , Mitsuo Yoshida , Masayuki Okabe , Kyoji Umemura

The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute…

Statistics Theory · Mathematics 2018-12-19 Luis Mendo

In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…

Statistics Theory · Mathematics 2025-03-20 Kenta Takatsu

Within the context of the binomial model, we analyse sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials…

Statistics Theory · Mathematics 2022-09-29 Ben O'Neill

The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…

Machine Learning · Statistics 2025-06-03 Ambrus Tamás , Balázs Csanád Csáji

We provide an asymptotic expression for the probability that a randomly chosen polynomial with given degree, having integral coefficients bounded by some B, has a prescribed signature. We also give certain related formulas and numerical…

Number Theory · Mathematics 2016-11-28 Csanád Bertók , Lajos Hajdu , Attila Pethő

Statistical analyses of multipopulation studies often use the data to select a particular population as the target of inference. For example, a confidence interval may be constructed for a population only in the event that its sample mean…

Statistics Theory · Mathematics 2025-09-18 Peter Hoff , Surya Tokdar

In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…

Statistics Theory · Mathematics 2013-11-05 Xinjia Chen

Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific…

Methodology · Statistics 2025-04-21 Ying Jin , Zhimei Ren