[Paper Review] SIHR: An R Package for Statistical Inference in High-dimensional Linear and Logistic Regression Models

Prabrisha Rakshit, Tommaso Cai+1 more|arXiv (Cornell University)|Sep 7, 2021

Statistical Methods and Inference22 references4 citations

TL;DR

This paper introduces SIHR, an R package for statistical inference in high-dimensional linear and logistic regression models. It enables point estimation, confidence interval construction, and hypothesis testing for linear and quadratic functionals using novel methods tailored to high-dimensional settings, with demonstrated performance on real data.

ABSTRACT

We introduce and illustrate through numerical examples the R package exttt{SIHR} which handles the statistical inference for (1) linear and quadratic functionals in the high-dimensional linear regression and (2) linear functional in the high-dimensional logistic regression. The focus of the proposed algorithms is on the point estimation, confidence interval construction and hypothesis testing. The inference methods are extended to multiple regression models. We include real data applications to demonstrate the package's performance and practicality.

Motivation & Objective

• Address the challenge of statistical inference in high-dimensional regression models where traditional methods fail due to high dimensionality.
• Develop a unified framework for inference on linear and quadratic functionals in high-dimensional linear regression.
• Extend inference capabilities to high-dimensional logistic regression models for binary outcomes.
• Enable multiple regression models with robust inference through point estimation, confidence intervals, and hypothesis testing.
• Demonstrate practical utility through real data applications to validate performance and usability.

Proposed method

• Propose a novel inference framework based on de-biased or desparsified estimators to handle high-dimensional parameter estimation with reduced bias.
• Construct confidence intervals for linear and quadratic functionals using asymptotic normality of the de-biased estimators.
• Implement hypothesis testing procedures via test statistics derived from the de-biased estimators, with proper scaling for high-dimensional variance.
• Extend the methodology to logistic regression by adapting the de-biasing approach to the non-Gaussian, binary outcome setting.
• Integrate all methods into a cohesive R package (SIHR) for user-friendly application and reproducibility.
• Support multiple regression models by generalizing inference procedures to multivariate functionals and joint parameter estimation.

Experimental results

Research questions

• RQ1 How can reliable statistical inference be performed in high-dimensional linear regression models with many predictors relative to sample size?
• RQ2 What is the performance of confidence intervals and hypothesis tests for linear and quadratic functionals in high-dimensional settings?
• RQ3 Can the de-biasing approach be effectively extended to logistic regression models with high-dimensional covariates?
• RQ4 How do the proposed inference methods compare in practice when applied to real-world datasets?
• RQ5 To what extent does the SIHR package support robust, reproducible inference across diverse high-dimensional regression scenarios?

Key findings

• The SIHR package successfully enables valid statistical inference for linear and quadratic functionals in high-dimensional linear regression models.
• Confidence intervals constructed using the de-biased estimators achieve appropriate coverage rates in finite samples, even under high dimensionality.
• Hypothesis testing procedures based on the proposed framework maintain correct Type I error rates under the null hypothesis.
• The extension to high-dimensional logistic regression allows for reliable inference on linear functionals despite non-Gaussian outcomes.
• Real data applications demonstrate the practical utility and robustness of the SIHR package in diverse high-dimensional settings.
• The package supports multiple regression models, enabling joint inference on multiple functionals with controlled error rates.