1
$\begingroup$

How can I relate $Var(y)$ with $Var(y)_{(i)}$ where $Var(y)_{(i)}$ is de variance of the data with the ith item removed. It is necesary first relate $\bar{y}$ with $\bar{y}_{(i)}$ and it complicates the variance relationship.

$\endgroup$
  • $\begingroup$ Is $y$ a scalar or a vector? And what do you mean with 'item'? $\endgroup$ – Stijn Dec 12 '14 at 19:34
  • $\begingroup$ Do you mean sample variance with full dataset versus one observation removed? $\endgroup$ – Adrian Dec 12 '14 at 19:41
  • $\begingroup$ Yes, y is the vector $y=(y_1, y_2, ..., y_i,...y_n)$ and $y_{(i)}$ is the vector $y_{(i)}=(y_1, y_2, ..., y_{i-1},y_{i+1}...y_n)$ with the i-th element removed $\endgroup$ – will198 Dec 12 '14 at 19:44
0
$\begingroup$

I think that I have found the solution by myself:

$Var(y)_{(i)}=\frac{n}{n-1}(Var(y)-\frac{(\bar{y}-y_i)^2}{(n-1)})$

Where:

  • $y_i$ is the i-th observation removed;

  • n is the number of observations in $y$;

  • $\bar{y}$ is de mean of $y$

$\endgroup$

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.