Confidence ellipsoid
= Confidence ellipsoid
{title2=$C=\{\theta:(\theta-\widehat\theta)^TA(\theta-\widehat\theta)\leq c\}$}
An ellipsoidal <confidence region> defined by a <positive-definite matrix> $A$ and a calibrated threshold $c$. For a known-covariance <multivariate normal distribution> sample, $A=n\Sigma^{-1}$ and the $1-\alpha$ quantile of the <chi-squared distribution> with $d$ <degrees of freedom> give exact coverage for the $d$-dimensional mean.