How accurately can one measure a statistical quantity like polarization-mode dispersion?

The differential group delay (DGD) due to varying local birefringence and random polarization mode coupling is a statistical quantity. Its value at any wavelength fluctuates in time. At any given moment it is wavelength sensitive. Hence, polarization-mode dispersion can only be defined as a mean or rms value of the DGD. All measurements of polarization-mode dispersion involve thus an averaging over a finite sample set. Consequently, all measurements are intrinsically of limited accuracy. We present analytical formulae and numerical data characterizing this intrinsic limitation common to all measurement techniques.