Consider the following contrived situation. Imagine a Gaussian white noise process $x[t]$, with bandwidth $Δf$, with PSD equal to some quantity $A$ which you would like to measure.
So the way to measure this seems to measure the variance of the process $x[t]$, which by Parseval's theorem will be $AΔf$.
So you measure points with some frequency $f_m$, probably $2Δf$. And at a lower rate, say $f_v$, you compute the variance of the preceding block of $f_m/f_v$ points and take that to be a measurement. What will the noise/variance be in this measurement of the variance of $x[t]$? How can I approach this question?