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.

  • $\begingroup$ 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

I think that I have found the solution by myself:



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

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

  • $\bar{y}$ is de mean of $y$


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