Related papers: Confidence Sets for a level set in linear regressi…
This paper develops a simple method to construct confidence bands, centered at a principal component analysis (PCA) based estimator, for the slope function in a functional linear regression model with a scalar response variable and a…
We develop a methodology for constructing confidence sets for parameters of statistical models via a reduction to sequential prediction. Our key observation is that for any generalized linear model (GLM), one can construct an associated…
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…
Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted…
The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then…
Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…
The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of…
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide…
A simple construction of adaptive confidence sets is proposed in isotonic, convex and unimodal regression. In univariate isotonic regression, the proposed confidence set enjoys uniform coverage over all non-decreasing regression functions.…
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…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
In this paper we consider the problem of constructing confidence intervals for coefficients of martingale regression models (in particular, time series models) after variable selection. Although constructing confidence intervals are common…
Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…
Datasets typically contain inaccuracies due to human error and societal biases, and these inaccuracies can affect the outcomes of models trained on such datasets. We present a technique for certifying whether linear regression models are…
Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null…
The goal of this paper is to indicate a new method for constructing normal confidence intervals for the mean, when the data is coming from stochastic structures with possibly long memory, especially when the dependence structure is not…
One of the most common problems preventing the application of prediction models in the real world is lack of generalization: The accuracy of models, measured in the benchmark does repeat itself on future data, e.g. in the settings of real…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…