0
$\begingroup$

The following is an example from a book (An Introduction to Pattern Recognition and Machine Learning by P. Fieguth, page 417) on random variables and random vectors. Please consider the following.

enter image description here

Question: What does this mean?:

"there are outliers present with a variance $\nu^2$ times as large as the sample variance."

Why $\nu^2$ times as large as the sample variance?

$\endgroup$

1 Answer 1

0
$\begingroup$

I think what this meant to say is " there are outliers present with a variance $v^2$ times as large as the variance of 90% of the sample" or something along those lines.

For $v^2=10$, $\hat{\sigma}=1.9$, so outlier distribution has ~5x the variance of sample. For $v^2=100$ $\hat{\sigma}=10.9$, outlier distribution has ~10x the sample variance, which is also the long run ratio for $v^2$ large, since 0.9 becomes negligible and only $\hat{\sigma} \propto v^2 / 10$ remains

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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