The two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2d −1 independent ways of defining a cumulative distribution function when d dimensions are involved. In this paper three variations on the Kolmogorov-Smirnov test for multi-dimensional data sets are surveyed: Peacock’s test [1] that computes in O(n3); Fasano and Franceschini’s test [2] that computes in O(n2); Cooke’s test that computes in O(n2). We prove that Cooke’s algorithm runs in O(n2), contrary to his claims that it runs in O(nlgn). We also compare these algorithms with ROOT’s version of the Kolmogorov-Smirnov test

Using R-based VOStat as a low resolution spectrum analysis tool

We describe here an online software suite VOStat written mainly for the Virtual Observatory, a novel structure in which astronomers share terabyte scale data. Written mostly in the public-domain statistical computing language and environment R, it can do a variety of statistical analysis on multidimensional, multi-epoch data with errors. Included are techniques which allow astronomers to start with multi-color data in the form of low-resolution spectra and select special kinds of sources in a variety of ways including color outliers. Here we describe the tool and demonstrate it with an example from Palomar-QUEST, a synoptic sky survey