High-Dimensional Inference: Confidence Intervals, $p$-Values and R-Software hdi

TL;DR

This paper reviews recent methods for high-dimensional inference, focusing on p-values and confidence intervals, and introduces the R-package hdi to facilitate their application and reproducibility.

Contribution

It provides a comprehensive review of recent high-dimensional inference techniques and introduces the hdi R-package for practical implementation.

Findings

Comparative empirical study of inference methods

Introduction of the hdi R-package for easy application

Enhanced reproducibility in high-dimensional inference

Abstract

We present a (selective) review of recent frequentist high-dimensional inference methods for constructing $p$-values and confidence intervals in linear and generalized linear models. We include a broad, comparative empirical study which complements the viewpoint from statistical methodology and theory. Furthermore, we introduce and illustrate the R-package hdi which easily allows the use of different methods and supports reproducibility.