I'm doing curve fitting, but my error is non-stationary. The variance decreases:

I'm looking for a signal in the noise (In this case at x=90, y=50).

I'd like to calculate the "standard error", and choose my signal be the point with the largest "standard error".

How do I do this when the variance is changing?

I'd appreciate someone providing the correct terminology/title/flags.

  • 1
    $\begingroup$ (x=90, y=50) looks like noise, not signal. An interesting question nevertheless. $\endgroup$ Commented Apr 25, 2023 at 6:11
  • $\begingroup$ @RichardHardy It's the output of a FFT, so pure signal would be a dirac delta $\endgroup$ Commented Apr 25, 2023 at 6:38
  • $\begingroup$ I ended up dealing with the heteroskedasticity by taking the log of y (the dependant variable). Its a well known technique statology.org/heteroscedasticity-regression $\endgroup$ Commented Apr 26, 2023 at 6:39
  • $\begingroup$ You need $y$ to be positive for that to work (a necessary but not a sufficient condition). How do the residuals look after having taken the log? Or even more interestingly, how did the data look before and after taking the log? (A 2x2 table of plots with data and residuals, raw and logged, would be nice.) $\endgroup$ Commented Apr 26, 2023 at 7:01
  • $\begingroup$ @RichardHardy here's a example without much noise for your curiosity. sqrt data, log data, log residuals. I've worked out the key to this problem is ensuring the noise only results are uniformly distributed. Right now they are normally distributed and this is biasing false positives (when their is a signal) toward it's centre $\endgroup$ Commented Apr 26, 2023 at 7:36


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