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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Covariance Estimation for Multivariate t Distribution</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for cov.trob {MASS}"><tr><td>cov.trob {MASS}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2> Covariance Estimation for Multivariate t Distribution </h2> <h3>Description</h3> <p>Estimates a covariance or correlation matrix assuming the data came from a multivariate t distribution: this provides some degree of robustness to outlier without giving a high breakdown point. </p> <h3>Usage</h3> <pre> cov.trob(x, wt = rep(1, n), cor = FALSE, center = TRUE, nu = 5, maxit = 25, tol = 0.01) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>data matrix. Missing values (NAs) are not allowed. </p> </td></tr> <tr valign="top"><td><code>wt</code></td> <td> <p>A vector of weights for each case: these are treated as if the case <code>i</code> actually occurred <code>wt[i]</code> times. </p> </td></tr> <tr valign="top"><td><code>cor</code></td> <td> <p>Flag to choose between returning the correlation (<code>cor = TRUE</code>) or covariance (<code>cor = FALSE</code>) matrix. </p> </td></tr> <tr valign="top"><td><code>center</code></td> <td> <p>a logical value or a numeric vector providing the location about which the covariance is to be taken. If <code>center = FALSE</code>, no centering is done; if <code>center = TRUE</code> the MLE of the location vector is used. </p> </td></tr> <tr valign="top"><td><code>nu</code></td> <td> <p>‘degrees of freedom’ for the multivariate t distribution. Must exceed 2 (so that the covariance matrix is finite). </p> </td></tr> <tr valign="top"><td><code>maxit</code></td> <td> <p>Maximum number of iterations in fitting. </p> </td></tr> <tr valign="top"><td><code>tol</code></td> <td> <p>Convergence tolerance for fitting. </p> </td></tr></table> <h3>Value</h3> <p>A list with the following components </p> <table summary="R valueblock"> <tr valign="top"><td><code>cov</code></td> <td> <p>the fitted covariance matrix. </p> </td></tr> <tr valign="top"><td><code>center</code></td> <td> <p>the estimated or specified location vector. </p> </td></tr> <tr valign="top"><td><code>wt</code></td> <td> <p>the specified weights: only returned if the <code>wt</code> argument was given. </p> </td></tr> <tr valign="top"><td><code>n.obs</code></td> <td> <p>the number of cases used in the fitting. </p> </td></tr> <tr valign="top"><td><code>cor</code></td> <td> <p>the fitted correlation matrix: only returned if <code>cor = TRUE</code>. </p> </td></tr> <tr valign="top"><td><code>call</code></td> <td> <p>The matched call. </p> </td></tr> <tr valign="top"><td><code>iter</code></td> <td> <p>The number of iterations used. </p> </td></tr></table> <h3>References</h3> <p>J. T. Kent, D. E. Tyler and Y. Vardi (1994) A curious likelihood identity for the multivariate t-distribution. <em>Communications in Statistics—Simulation and Computation</em> <b>23</b>, 441–453. </p> <p>Venables, W. N. and Ripley, B. D. (1999) <em>Modern Applied Statistics with S-PLUS.</em> Third Edition. Springer. </p> <h3>See Also</h3> <p><code><a href="../../stats/html/cor.html">cov</a></code>, <code><a href="../../stats/html/cov.wt.html">cov.wt</a></code>, <code><a href="cov.rob.html">cov.mve</a></code> </p> <h3>Examples</h3> <pre> cov.trob(stackloss) </pre> <hr /><div style="text-align: center;">[Package <em>MASS</em> version 7.3-51.4 <a href="00Index.html">Index</a>]</div> </body></html>