Related papers: High-Confident Nonparametric Fixed-Width Uncertain…
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…
We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…
This work develops central limit theorems for cross-validation and consistent estimators of its asymptotic variance under weak stability conditions on the learning algorithm. Together, these results provide practical, asymptotically-exact…
The batch means estimator of the MCMC variance is a simple and effective measure of accuracy for MCMC based ergodic averages. Under various regularity conditions, the estimator has been shown to be consistent for the true variance. However,…
Vertically weighted averages perform a bilateral filtering of data, in order to preserve fine details of the underlying signal, especially discontinuities such as jumps (in dimension one) or edges (in dimension two). In homogeneous regions…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We address the classical problem of constructing confidence intervals (CIs) for the mean of a distribution, given \(N\) i.i.d. samples, such that the CI contains the true mean with probability at least \(1 - \delta\), where \(\delta \in…
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 paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on…
This paper develops a method to construct uniform confidence bands for a nonparametric regression function where a predictor variable is subject to a measurement error. We allow for the distribution of the measurement error to be unknown,…
A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
We introduce a new framework for creating point-wise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our framework is based on binomial properties and motivates…
Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We…
This paper is concerned with estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its…
For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a…
This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many…
Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…