vcovA

Estimate the variance-covariance matrix of the joint (VaR, ES) estimator by the sandwich formula:
$$\lambda^{-1} \Sigma \lambda^{-1}$$
Several estimators are available for both matrices and the default options are selected to take into account
possible misspecifications in the underlying data.

Simultaneous modeling of the quantile and the expected shortfall of a response variable given
a set of covariates, see Dimitriadis and Bayer (2019) <doi:10.1214/19-EJS1560>.

Sebastian Bayer

esreg

Joint Quantile and Expected Shortfall Regression

Timo Dimitriadis

vcovA function

<dl><dt>object</dt>
<dd>An esreg object</dd>
<dt>sigma_est</dt>
<dd>The estimator to be used for $\Sigma$, see conditional_truncated_variance<ul>
<li>ind - Variance over all negative residuals</li>
<li>scl_N - Scaling with the normal distribution</li>
<li>scl_sp - Scaling with the kernel density function</li>
</ul></dd>
<dt>sparsity</dt>
<dd>The estimator to be used for the sparsity in $\Lambda$, see density_quantile_function<ul>
<li>iid - Piecewise linear interpolation of the distribution</li>
<li>nid - Hendricks and Koenker sandwich</li>
</ul></dd>
<dt>misspec</dt>
<dd>if TRUE, the estimator accounts for potential misspecification in the model</dd>
<dt>bandwidth_estimator</dt>
<dd>The bandwidth estimator to be used for the iid and nid sparsity estimator, see density_quantile_function<ul>
<li>Bofinger</li>
<li>Chamberlain</li>
<li>Hall-Sheather</li>
</ul></dd></dl>

Arguments

Asymptotic Covariance Estimation — vcovA

<dl>

<dt>object</dt>
<dd>An esreg object</dd>


<dt>sigma_est</dt>
<dd>The estimator to be used for $\Sigma$, see conditional_truncated_variance<ul>
<li>ind - Variance over all negative residuals</li>
<li>scl_N - Scaling with the normal distribution</li>
<li>scl_sp - Scaling with the kernel density function</li>
</ul></dd>


<dt>sparsity</dt>
<dd>The estimator to be used for the sparsity in $\Lambda$, see density_quantile_function<ul>
<li>iid - Piecewise linear interpolation of the distribution</li>
<li>nid - Hendricks and Koenker sandwich</li>
</ul></dd>


<dt>misspec</dt>
<dd>if TRUE, the estimator accounts for potential misspecification in the model</dd>


<dt>bandwidth_estimator</dt>
<dd>The bandwidth estimator to be used for the iid and nid sparsity estimator, see density_quantile_function<ul>
<li>Bofinger</li>
<li>Chamberlain</li>
<li>Hall-Sheather</li>
</ul></dd>

</dl>

vcovA: Asymptotic Covariance Estimation

Description

Usage

Arguments