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August 27th, 2018, 01:52 AM  #1 
Newbie Joined: Jun 2017 From: italia Posts: 13 Thanks: 2  Distributionfree test for outliers
My data are obtained by subtracting two vector $V_{1}$ and $V_{2}$ in a 3D space: $$v=\sqrt{(V_{1_{x}}V_{2_{x}})^2+(V_{1_{y}}V_{2_{y}})^2+(V_{1_{z}}V_{2_{z}})^2}$$ I don't know the distribution of $v$, but it vaguely resembles a very longtailed lognormal distribution. Without any valid assumption, I assume an unknown distribution. My current method to find the outliers is based on the Chebyshevâ€™s inequality; I say that $v$ is an outlier if $v\bar{v} > 10 s$ (sample average and sample standard deviation). Could that method be reasonably valid? I found a paper that explains the Bootlier test to find outliers: https://www.econstor.eu/bitstream/10.../735352828.pdf, but it's not clear to me how to write a working procedure for that test. Please, could anyone explain the Bootlier test in practical terms? 
August 27th, 2018, 04:16 AM  #2  
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174  Quote:
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The bootlier is a good test, and there are R scripts written to make it work. Definitely don't write your own script, the procedures you can find online usually do the job very well. https://github.com/jodeleeuw/Bootlie...ter/bootlier.R Notice the bootlier does work well with skewed distributions, but only if you have quite a generous amount of data points. Another method you might want to try are isolation forests. This is also nondistributional and works quite well. There are a lot of methods on finding outliers nondistributionally, but I really like these two.  
August 27th, 2018, 05:32 AM  #3  
Newbie Joined: Jun 2017 From: italia Posts: 13 Thanks: 2  Quote:
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