相关论文: Adaptive nonparametric confidence sets

A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…

We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales,…

Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…

Recent advances in statistics introduced versions of the central limit theorem for high-dimensional vectors, allowing for the construction of confidence regions for high-dimensional parameters. In this note, $s$-sparsely convex…

Machine learning models trained on uncurated datasets can often end up adversely affecting inputs belonging to underrepresented groups. To address this issue, we consider the problem of adaptively constructing training sets which allow us…

We introduce a new $hp$-adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approach is based on a generally applicable prediction strategy…

We design a general framework for answering adaptive statistical queries that focuses on providing explicit confidence intervals along with point estimates. Prior work in this area has either focused on providing tight confidence intervals…

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…

We consider clinical trials in which an experimental treatment is compared with a control in pre-specified patient subpopulations. In such settings, adaptive enrichment designs allow the enrolled population to be modified at an interim…

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…

This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…

Confidence region prediction is a practically useful extension to the commonly studied pattern recognition problem. Instead of predicting a single label, the constraint is relaxed to allow prediction of a subset of labels given a desired…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…

In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…

While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…

We consider the problem of adaptive estimation of the regression function in a framework where we replace ergodicity assumptions (such as independence or mixing) by another structural assumption on the model. Namely, we propose adaptive…

Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…

Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…