Suppose two time series (of light flux). The goal is to determine whether the series are from the same distribution. It is usual to use the Kolmogorov-Smirnov (KS) test in this situation.

However, the times intervals are not necessarily even between the measurements, as some data may be missing. Is it correct to deduce that the test must then be on two-dimensional arrays of (time, flux)?

However, because of Why can't one generalize the Kolmogorov-Smirnov test to 2 or more dimensions?, one would use KS for two-dimensional arrays. So Beware the Kolmogorov-Smirnov test! suggests the Anderson-Darling (AD) test with bootstrap.

In IDL, would bootstrap.pro do the job? And then edf_stats-code.pro for the AD test? Can bootstrap.pro be understood as preparing the data for the test as written in edf_stats-code.pro?

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    $\begingroup$ I am puzzled by the conjunction of time series and distributional tests. The latter ignores the time element altogether, so questions about the spacing of measurements would seem irrelevant and it seems that you are in a standard setting of comparing one batch of data to another batch. The issue of missing data is a separate one which can be addressed independently--but if you use time-series methods to impute the missing data, you are already assuming your datasets are not groups of independent results, which greatly complicates the distributional testing. $\endgroup$
    – whuber
    Jun 30, 2014 at 20:54
  • $\begingroup$ I suppose that one can refer to en.wikipedia.org/wiki/Missing_data for the missing data issue. However, the data is still time-dependent because it is paired, before and after an event (my original question makes no mention of this). For more clarity, there are two pairs of batches of data to compare. Of course, I would prefer taking the pairing into account, if possible... which it should be? $\endgroup$ Jun 30, 2014 at 21:13


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