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Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this work, for the first time, we apply conformal-prediction to…

Nuclear Theory · Physics 2026-02-02 Habib Yousefi Dezdarani , Ryan Curry , Alexandros Gezerlis

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to…

Statistics Theory · Mathematics 2008-08-08 Zhibiao Zhao , Wei Biao Wu

Inference via simultaneous confidence band is studied for stationary covariance function of dense functional data. A two-stage estimation procedure is proposed based on spline approximation, the first stage involving estimation of all the…

Methodology · Statistics 2019-10-31 Jiangyan Wang , Guanqun Cao , Li Wang , Lijian Yang

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

Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for…

Machine Learning · Statistics 2026-01-27 Balázs Csanád Csáji , Bálint Horváth

In this paper we develop procedures to construct simultaneous confidence bands for $\tilde p$ potentially infinite-dimensional parameters after model selection for general moment condition models where $\tilde p$ is potentially much larger…

Methodology · Statistics 2019-02-05 Alexandre Belloni , Victor Chernozhukov , Denis Chetverikov , Ying Wei

The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of…

Machine Learning · Statistics 2024-01-30 Balázs Csanád Csáji , Bálint Horváth

We propose simultaneous confidence bands of the hyperbolic-type for the contrasts between several nonlinear (curvilinear) regression curves. The critical value of a confidence band is determined from the distribution of the maximum of a…

Statistics Theory · Mathematics 2017-01-11 Xiaolei Lu , Satoshi Kuriki

This paper develops a method to construct uniform confidence bands in deconvolution when the error distribution is unknown. We mainly focus on the baseline setting where an auxiliary sample from the error distribution is available and the…

Statistics Theory · Mathematics 2017-07-25 Kengo Kato , Yuya Sasaki

We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. Our method integrates sieve…

Methodology · Statistics 2024-04-24 Philipp Bach , Sven Klaassen , Jannis Kueck , Martin Spindler

Bandpass filtering techniques are widely used in spectroscopy. However, conventional symmetric-padding filtering methods introduce boundary artifacts that distort the signal at the edges. We present a rubber band filter: a robust method for…

Optics · Physics 2025-07-11 Zhenyang Xiao , David Burghoff

The focus of this paper is on the quantification of sampling variation in frequentist probabilistic forecasts. We propose a method of constructing confidence sets that respects the functional nature of the forecast distribution, and use…

Methodology · Statistics 2017-08-09 David Harris , Gael M. Martin , Indeewara Perera , D. S. Poskitt

Uniform confidence bands for functions are widely used in empirical analysis. A variety of simple implementation methods (most notably multiplier bootstrap) have been proposed and theoretically justified. However, an implementation over a…

Methodology · Statistics 2025-12-23 Shunsuke Imai

Deep learning models have significantly improved prediction accuracy in various fields, gaining recognition across numerous disciplines. Yet, an aspect of deep learning that remains insufficiently addressed is the assessment of prediction…

Machine Learning · Statistics 2024-12-18 Asaf Ben Arie , Malka Gorfine

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the…

Statistics Theory · Mathematics 2010-06-16 Jean-Christophe Breton , Jean-François Coeurjolly

We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…

Methodology · Statistics 2025-02-06 Michael Stanley , Pau Batlle , Pratik Patil , Houman Owhadi , Mikael Kuusela

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

We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine…

Statistics Theory · Mathematics 2020-09-07 Timothy B. Armstrong

We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…

Statistics Theory · Mathematics 2025-03-04 John C. Duchi

Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the…

Optimization and Control · Mathematics 2019-01-09 Xi Chen , Qihang Lin , Guanglin Xu