# #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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