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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper investigates correct variable selection in finite samples via$\ell_1$ and $\ell_1+\ell_2$ type penalization schemes. The asymptoticconsistency of variable selection immediately follows from this analysis. Wefocus on logistic and linear regression models. The following questions arecentral to our paper: given a level of confidence $1-\delta$, under whichassumptions on the design matrix, for which strength of the signal and for whatvalues of the tuning parameters can we identify the true model at the givenlevel of confidence? Formally, if $\widehat{I}$ is an estimate of the truevariable set $I^*$, we study conditions under which$\mathbb{P}(\widehat{I}=I^*)\geq 1-\delta$, for a given sample size $n$, numberof parameters $M$ and confidence $1-\delta$. We show that in identifiablemodels, both methods can recover coefficients of size $\frac{1}{\sqrt{n}}$, upto small multiplicative constants and logarithmic factors in $M$ and$\frac{1}{\delta}$. The advantage of the $\ell_1+\ell_2$ penalization over the$\ell_1$ is minor for the variable selection problem, for the models weconsider here. Whereas the former estimates are unique, and become more stablefor highly correlated data matrices as one increases the tuning parameter ofthe $\ell_2$ part, too large an increase in this parameter value may precludevariable selection.

Honest variable selection in linear and logistic regression models via $\ell_1$ and $\ell_1+\ell_2$ penalization