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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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

Lucas Janson, Rina Foygel Barber, Emmanuel Candès

Journal of the Royal Statistical Society. Series B, Statistical Methodology

|November 7, 2017

Summary

A new method, EigenPrism, provides accurate confidence intervals for high-dimensional regression problems, unifying inference for error, noise level, and genetic heritability. It

Keywords:

EigenPrism Heritability Regression error Signal-to-noise ratio Variance estimation

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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.