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Related papers: Optimal Confidence Bands for Shape-restricted Regr…

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We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…

Machine Learning · Statistics 2023-01-18 Tengyuan Liang

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

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…

Statistics Theory · Mathematics 2016-04-06 Lucy Kerns

We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares…

Econometrics · Economics 2024-01-09 Xiaohong Chen , Timothy Christensen , Sid Kankanala

We propose an optimal experimental design for a curvilinear regression model that minimizes the band-width of simultaneous confidence bands. Simultaneous confidence bands for curvilinear regression are constructed by evaluating the volume…

Statistics Theory · Mathematics 2019-04-02 Satoshi Kuriki , Henry P. Wynn

The choice of hyperparameters greatly impacts performance in natural language processing. Often, it is hard to tell if a method is better than another or just better tuned. Tuning curves fix this ambiguity by accounting for tuning effort.…

Computation and Language · Computer Science 2024-04-10 Nicholas Lourie , Kyunghyun Cho , He He

This paper presents a method for constructing uniform confidence bands for the marginal treatment effect (MTE) function. The shape of the MTE function offers insight into how the unobserved propensity to receive treatment is related to the…

Econometrics · Economics 2025-09-23 Toshiki Tsuda , Yanchun Jin , Ryo Okui

Ordinary differential equation (ODE) is an important tool to study the dynamics of a system of biological and physical processes. A central question in ODE modeling is to infer the significance of individual regulatory effect of one signal…

Methodology · Statistics 2024-02-06 Xiaowu Dai , Lexin Li

When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected…

Statistics Theory · Mathematics 2013-12-12 Hervé Cardot , David Degras , Etienne Josserand

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

Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly…

Methodology · Statistics 2021-04-13 Jacopo Diquigiovanni , Matteo Fontana , Simone Vantini

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

Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the…

Statistics Theory · Mathematics 2021-06-08 Stefan Bedbur , Fabian Mies

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

Statistics Theory · Mathematics 2022-11-24 Kang Wang , Subhashis Ghosal

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 this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a…

Methodology · Statistics 2019-06-06 Gang Cheng , Yen-Chi Chen

This article presents methods for constructing an asymptotic hyperbolic band under the multiple logistic regression model when the predictor variables are restricted to a specific region $\mathscr{X}$. Scheff\'{e}'s method yields…

Statistics Theory · Mathematics 2016-04-06 Lucy Kerns

We develop a novel method of constructing confidence bands for nonparametric regression functions under shape constraints. This method can be implemented via a linear programming, and it is thus computationally appealing. We illustrate a…

Econometrics · Economics 2021-02-15 Harold D. Chiang , Kengo Kato , Yuya Sasaki , Takuya Ura

Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…

Statistics Theory · Mathematics 2014-01-30 Peter Hall , Joel Horowitz

We construct confidence sets for the regression function in nonparametric binary regression with an unknown design density. These confidence sets are adaptive in $L^2$ loss over a continuous class of Sobolev type spaces. Adaptation holds in…

Statistics Theory · Mathematics 2016-08-04 Rajarshi Mukherjee , Subhabrata Sen