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Re: Kolmogorov Smirnov in two or more dimensions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124839] Re: Kolmogorov Smirnov in two or more dimensions
  • From: Andy Ross <andyr at wolfram.com>
  • Date: Thu, 9 Feb 2012 05:36:36 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201202081032.FAA06541@smc.vnet.net>

This is a bug in KolmogorovSmirnovTest that will be fixed in later 
versions of Mathematica. For the time being you can use 
CramerVonMisesTest or DistributionFitTest.

Note that DistributionFitTest uses a little known test referred to as 
Szekely-Energy. A description can be found in...

Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal Distributions 
in High Dimension, InterStat,
November (5)

P-values for this test are computed via Monte-Carlo simulation at the 
moment so it tends to be slow.

The good thing about this test is that it doesn't just look at things 
marginally.  All of the other tests currently available perform tests on 
the marginal data and then aggregate the statistics. Thus any 
differences in covariance structure will be missed.

The take home message is that if things don't fit marginally then they 
don't fit jointly but if they do seem to fit well marginally you still 
need to dig deeper to determine whether the joint distributions are 
equivalent.

Andy Ross
Wolfram Research

On 2/8/2012 4:32 AM, maria giovanna dainotti wrote:
> Dear Mathematica group,
> I am doing an analysis of the Kolmogorov with two data sets of 2 dimensions each.
> When I apply the KolmogorovSmirnovTest[Data0,Data0] I should get 1. I did just a trial and I got 0.
> I am copying the datafile example for clarity.
> {{0.97304, 14.1829}, {0.98663, 14.1295}, {0.98284, 14.3172}, {0.81423,
>     14.3466}, {0.97303, 14.5966}, {0.87122, 14.8435}, {0.90252,
>    14.9036}, {0.81887, 15.1177}, {1.07722, 14.6849}, {0.86684,
>    15.6456}, {0.86664, 14.7034}, {0.78728, 15.0898}, {1.10336,
>    14.4085}, {1.12014, 14.7281}, {0.95923, 14.4988}, {0.89942,
>    15.3173}, {0.83841, 14.8422}, {0.99105, 14.8813}, {1.111,
>    14.5964}, {0.93255, 15.5019}, {1.03142, 14.8009}, {1.00661,
>    15.0827}, {0.93255, 15.3064}, {1.10023, 14.7189}, {0.8797,
>    15.1038}, {1.0013, 14.6755}, {0.87673, 15.0952}, {0.84131,
>    15.7345}, {1.06392, 15.3528}, {1.00138, 14.9835}, {0.77803,
>    15.4637}, {0.76795, 15.3611}, {0.98328, 15.1047}, {0.89193,
>    14.8321}, {0.72882, 15.909}, {0.77123, 15.7902}, {0.86218,
>    15.6637}, {0.84381, 15.536}, {0.99263, 15.8903}, {1.0805,
>    15.1453}, {0.85316, 15.7793}, {0.85186, 15.9119}, {1.10898,
>    15.7583}, {1.03365, 15.7393}, {0.84783, 16.1911}, {1.10979,
>    16.0031}, {1.05238, 16.015}, {0.90259, 16.4864}, {0.84963,
>    15.9818}, {1.09221, 16.0088}, {1.0443, 15.8326}, {0.8945,
>    16.1927}, {0.83015, 16.2776}, {0.7551, 16.5538}, {1.05947,
>    15.9138}, {1.06189, 15.6061}, {1.05889, 16.0743}, {0.85216,
>    16.1568}, {0.72597, 16.7657}, {0.93638, 16.3583}, {0.81968,
>    16.2711}, {0.95022, 16.3549}, {1.04536, 16.18}, {1.0786,
>    16.0967}, {0.9385, 15.8504}, {0.95024, 15.9338}, {0.76753,
>    17.1461}, {1.18224, 16.0437}, {0.96447, 16.4908}, {0.98235,
>    16.0892}, {1.06151, 16.699}, {0.79052, 16.5207}, {1.15863,
>    16.3223}, {1.00795, 16.2444}, {1.07284, 16.6536}, {1.04796,
>    16.865}, {0.84226, 16.7247}, {1.04712, 16.2673}}
>
> Or maybe should I use some other conditions?
> Or if it doesn't work is there an already built package that I can use?
>
> Thanks a lot for your help
>
> Best regards,
> Maria




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