EigenPrism: inference for high dimensional signal-to-noise ratios

Area of Science:

• Statistical Inference
• High-Dimensional Statistics
• Genomics

Background:

• Constructing confidence intervals for high-dimensional regression is challenging.
• Existing methods often require assumptions on sparsity or noise level knowledge.

Purpose of the Study:

• To develop a unified statistical inference procedure for high-dimensional regression.
• To address confidence interval construction for regression error, noise level, and genetic signal-to-noise ratio.

Main Methods:

• Introduced a novel procedure, EigenPrism, for inference on the signal norm in high-dimensional linear regression.
• Developed asymptotically correct intervals for Gaussian covariates, valid in finite samples.
• Demonstrated unification of three key statistical inference problems.

Main Results:

• EigenPrism provides valid confidence intervals with minor modifications for three distinct problems.
• The method is computationally fast and makes no assumptions on coefficient sparsity or noise level.
• Confidence intervals show robustness in coverage beyond Gaussian covariates.

Conclusions:

• EigenPrism offers a unified and efficient approach to statistical inference in high-dimensional settings.
• The method has practical applications, including genetic data analysis for heritability estimation.
• EigenPrism's performance is comparable to Bayesian methods, with intervals only 5% wider.