awgl_omega

Internal function: Quantile regression with adaptively group Lasso with <code>Omega</code>.

internal

Implements an adaptively weighted group Lasso procedure for simultaneous variable selection and structure identification in varying
coefficient quantile regression models and additive quantile regression models with ultra-high dimensional covariates. The methodology, grounded
in a strong sparsity condition, establishes selection consistency under certain weight conditions. To address the challenge of tuning parameter
selection in practice, a BIC-type criterion named high-dimensional information criterion (HDIC) is proposed. The Lasso procedure, guided by
HDIC-determined tuning parameters, maintains selection consistency. Theoretical findings are strongly supported by simulation studies.
(Toshio Honda, Ching-Kang Ing, Wei-Ying Wu, 2019, <DOI:10.3150/18-BEJ1091>).

Wen-Ting Wang

QuantRegGLasso

Adaptively Weighted Group Lasso for Semiparametric Quantile
Regression Models

Wei-Ying Wu

Toshio Honda

Ching-Kang Ing

awgl_omega function

<dl><dt>Y</dt>
<dd>Data matrix (\(n \times 1\)).</dd>
<dt>W</dt>
<dd>B-splines with covariates matrix with \(p \times L\) columns and \(n\) rows.</dd>
<dt>omega</dt>
<dd>Weights for group lasso.</dd>
<dt>lambda</dt>
<dd>A sequence of tuning parameters.</dd>
<dt>tau</dt>
<dd>A quantile of interest.</dd>
<dt>qn</dt>
<dd>A bound parameter for HDIC.</dd>
<dt>zeta</dt>
<dd>A step parameter.</dd>
<dt>zetaincre</dt>
<dd>An increment of each step.</dd>
<dt>maxit</dt>
<dd>The maximum number of iterations.</dd>
<dt>tol</dt>
<dd>A tolerance rate.</dd></dl>

Arguments

Internal function: Quantile Regression with Adaptively Group Lasso with Omega — awgl_omega

<dl>

<dt>Y</dt>
<dd>Data matrix (\(n \times 1\)).</dd>


<dt>W</dt>
<dd>B-splines with covariates matrix with \(p \times L\) columns and \(n\) rows.</dd>


<dt>omega</dt>
<dd>Weights for group lasso.</dd>


<dt>lambda</dt>
<dd>A sequence of tuning parameters.</dd>


<dt>tau</dt>
<dd>A quantile of interest.</dd>


<dt>qn</dt>
<dd>A bound parameter for HDIC.</dd>


<dt>zeta</dt>
<dd>A step parameter.</dd>


<dt>zetaincre</dt>
<dd>An increment of each step.</dd>


<dt>maxit</dt>
<dd>The maximum number of iterations.</dd>


<dt>tol</dt>
<dd>A tolerance rate.</dd>

</dl>

awgl_omega: Internal function: Quantile Regression with Adaptively Group Lasso with `Omega`

Description

Usage

Value

Arguments