I am averaging periodograms from sets of ~15-25 experimentally measured timeseries all of the same length. To do this I am just summing the power in each frequency bin over all periodograms and then dividing by the total power over all the periodograms (I believe this is similar to Welch's Method but here I have many timeseries instead of a single long timeseries).
In many of these averaged periodograms I see a distinct peak that is called as statistically significant by Fisher's G-test. What is a good way to get a confidence interval or other interval estimate (e.g. standard-error of the mean) for the frequency of this peak? Is there some method that takes into account both sample size and width of the peak (maybe width at half-max)?
Add note below to provide more detail:
These are real timeseries data from measurements of gene expression in cells (each timeseries is the gene expression in an individual cell sampled every 6 minutes for ~10 hrs). I have been averaging the individual periodograms to create an averaged periodogram (like Bartlett's method) and want to be able to determine two things:
i.) Is a power at a frequency in the averaged periodogram statistically significant (i.e. unlikely to be due to chance)? This is what I am currently using Fisher's G-Test for but if there are better methods I am open to trying those (provided I can understand them and they are relatively easy to use).
ii.) What is an interval estimate for the frequency of a statistically significant power in the averaged periodogram? The bin with the greatest power in these averaged periodograms is typically a "peak" (when a line is plotted connecting the power values across bins) with neighboring bins also showing some increased power relative to other parts of the periodogram.