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Conformal prediction is a model-free machine learning method for constructing prediction regions at a guaranteed coverage probability level. However, a data scientist often faces three challenges in practice: (i) the determination of a…
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal…
In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In…
Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
This paper focuses on a semiparametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We develop a collection of methods for adjusting the predictions of quantile regression to ensure coverage. Our methods are model agnostic and can be used to correct for high-dimensional overfitting bias with only minimal assumptions.…
We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
In fields that are mainly nonexperimental, such as economics and finance, it is inescapable to compute test statistics and confidence regions that are not probabilistically independent from previously examined data. The Bayesian and…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…
As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…
This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…