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Problem

Visually, the "extreme" outliers in the following graph are somewhat obvious:

http://i.imgur.com/tiSbS.png

Question

Given:

  • T - Set of all temperatures
  • Y - Set of all years
  • ΣT - Sum of temperatures.
  • ΣY - Sum of years.
  • N - Number of elements
  • T(n) - Temperature of the nth element in the temperature set

How do you determine if T(n) is an outlier?

Related Sites

The math on some of these sites is a bit above my understanding:

Many thanks!

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Although I find the question to be interesting and profound, I removed the set-theory tag, since I don't find it applicable. Perhaps the question could be further retagged? –  Joel David Hamkins May 10 '10 at 2:40
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If you are looking for practical approaches to outlier removal, you might like to read the answers to mathoverflow.net/questions/6819/…. If you are interested in a philosophical discussion about when it is appropriate to remove outliers (if it ever is) then it appears that Joel might be interested in such a discussion -). –  Robby McKilliam May 10 '10 at 3:41
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2 Answers

up vote 1 down vote accepted

I might suggest LTS, the Least Trimmed Squares, approach. there is code in fortran and matlab, the latter called fastlts, both produced, I believe, by Rousseuw's group. The method essentially minimizes the error of fit for a proportion of the data points, with the rest (outliers) ignored. The outliers are found by something like the Minimum Volume Ellipsoid method (roughly, find the ellipsoid of minimum volume containing 1/2 the points).

hth,

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Douglas Hawkins' book Identification of Outliers is not up to date unless it's been edited since last I looked, but it might give you some idea of the issues involved, no awareness of which is apparent in Steven Pav's answer.

(BTW, I'd have called this a one-variable linear regression; I was surprised to see what it was, given the subject heading.)

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