Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$.  I'm trying to figure out $Var(Y)$ and its sampling error.

I thought I could just calculate $Var(Y) = Var(Z) - Var(X)$ and use the sum of the sampling variances to produce the variance related to the final error, but the process breaks down when B is small or might not exist, occasionally resulting in a negative difference that has no meaning to me as a variance.  That is, $Var(Z) - Var(X) < 0$ possibly due to sampling error.

When this difference is negative, it seems either the proposition that B is a sum with A is false, or simply that the real value is close to zero and not enough samples have been taken to get the measured result close enough to zero yet.

Is there a way to determine the likelihood that the proposition is false or true when the measured value is very negative?