What is the meaning of the quantity:


Is there, for example, a geometric explanation? Is there a term for it in statistics?

  • $\begingroup$ if the answer ok for you @apadana, can you please accept and/or upvote it? $\endgroup$
    – gunes
    Mar 26 '20 at 20:50

It is the square root of the determinant of the covariance matrix (between $X$ and $P$). The determinant of the covariance matrix is called as Generalized Variance, which quantifies the co-variability of multivariate random variables to a scalar. What you write is the square root of it, so I believe it won't be too odd to call it as Generalized Deviation.

Edit: After some research, I found that, in some contexts, it's referred as Generalized Standard Deviation, or Wilk's standard deviation.

  • $\begingroup$ Have you seen "generalized deviation" used anywhere, or did you come up with that term? $\endgroup$
    – Dave
    Mar 11 '20 at 18:22
  • $\begingroup$ @Dave I've come up with it actually. $\endgroup$
    – gunes
    Mar 11 '20 at 21:22
  • 1
    $\begingroup$ "Co-variability" is more accurate, than "variability". E.g. if the determinant of a covariance matrix is zero, there's linear dependence among the de-meaned random variables. (In the two by two case here, $\epsilon = 0$ if and only if $X$ lies in the linear span of $P$ and $1$.) $\endgroup$
    – Michael
    Mar 12 '20 at 1:28
  • $\begingroup$ Right @Michael changed it $\endgroup$
    – gunes
    Mar 12 '20 at 7:32

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.