Summary form only given. Optical near-field photoluminescence as well as microphotoluminescence spectra often show many tens of sharp lines in each local spectrum. Just by looking at such huge data sets, it is generally rather difficult to extract relevant information of the sample properties. Thus, the recent theoretical prediction of Runge and Zimmermann (1998), to use the averaged autocorrelations of individual local optical spectra in order to reveal hidden spectral correlations, has opened a new route towards statistical analysis. This statistical procedure was applied and modified by us quite recently in such a way that it becomes suitable for typical experimental spectra. We apply the technique to a single high-quality, growth-interrupted, thin fihn GaAs clad between AlAs/GaAs superlattice barriers. The quantum well is only 30 nm away from the surface, which allows to access the optical near-field. Our statistical analysis is based on a total of about 160,000 low-temperature optical near-field spectra, measured in about 100 sets. The spectra are normalized to equal spectral integral, their average is subtracted, the individual autocorrelation functions are computed and averaged. The resulting correlation function, would show no structures if the sharp lines in the spectra were just randomly distributed.