English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Variable selection properties of procedures utilizing penalized-likelihoodestimates is a central topic in the study of high dimensional linear regressionproblems. Existing literature emphasizes the quality of ranking of thevariables by such procedures as reflected in the receiver operatingcharacteristic curve or in prediction performance. Specifically, recent workshave harnessed modern theory of approximate message-passing (AMP) to obtain, ina particular setting, exact asymptotic predictions of the type I-type II errortradeoff for selection procedures that rely on $\ell_{p}$-regularizedestimators. In practice, effective ranking by itself is often not sufficientbecause some calibration for Type I error is required. In this work we studytheoretically the power of selection procedures that similarly rank thefeatures by the size of an $\ell_{p}$-regularized estimator, but further useModel-X knockoffs to control the false discovery rate in the realisticsituation where no prior information about the signal is available. Inanalyzing the power of the resulting procedure, we extend existing results inAMP theory to handle the pairing between original variables and theirknockoffs. This is used to derive exact asymptotic predictions for power. Weapply the general results to compare the power of the knockoffs versions ofLasso and thresholded-Lasso selection, and demonstrate that in the i.i.d.covariate setting under consideration, tuning by cross-validation on theaugmented design matrix is nearly optimal. We further demonstrate how thetechniques allow to analyze also the Type S error, and a corresponding notionof power, when selections are supplemented with a decision on the sign of thecoefficient.

A Power Analysis for Model-X Knockoffs with $\ell_{p}$-Regularized Statistics