#StackBounty: #estimation #inference #standard-error Standard error of estimated covariance

Bounty: 50

Let $X_1,…,X_n$ and $Y_1,…,Y_n$ be two independent random samples from $mathcal{N}(mu, sigma^2)$ where both $mu$ and $sigma$ are unknown parameters.

I estimate their covariance using:
$$hat{operatorname{cov}}(X, Y) = operatorname{E}{big[(X_i – operatorname{E}[X])(Y_i – operatorname{E}[Y])big]} $$

with replacing $operatorname{E}[X]$ and $operatorname{E}[Y]$ by the according sample mean.

How do i calculate the standard error of $hat{operatorname{cov}}(X, Y)$?


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