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AMDA-2008-Session 11

# AMDA-2008-Session 11 - ROBUST STATISTICS OUTLIER RESISTANT...

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ROBUST STATISTICS OUTLIER RESISTANT METHODS

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What is an Oultier? An outlying observation, or ‘outlier’ is one that appears to deviate markedly from other members of the sample in which it occurs. Example: 2, 3, 6, 2, 3, 100, 5, 2 The observation 100 is markedly different from the rest. This is an outlier
How outliers occur? Outliers can occur due to: Human errors in recording and/ or measurement Application of an incorrect probability model for data.

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How to deal with outliers? Identify the outliers through careful screening of the data and use of some statistical tests (discordancy tests). Subsequently delete these observations and apply standard statistical procedures. Use methods that are ‘outlier resistant’. These methods are called robust methods.
Box-Plot Consider univariate data. We can compute the five number summary of the data (Min, Q , Median, Q , Max). These numbers can be given in a plot as shown. 0.98 0.99 1.00 1.01 1.02

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Effect of outliers on estimators: Influence Function ( 29 1. ) P(X i.e. at degenerate is G where ) ( ) 1 ( lim ) ( IC is F on distributi basic at the T estimator an of function influence The 0 F T, = = - + - = ξ ξ λ λ λ ξ λ F T G F T
Influence Function of the Mean robust. not is T say we Hence ) ( lim ) ( )) ( ( lim ) ( ) ( ) 1 ( lim ) ( )) ( ) ( ) 1 (( lim ) ( E(X). xdF(x) T(F) Let , 0 0 } { 0 , - = - = - = - + - = - + - = = = - - ξ ξ λ ξ λ λ λξ λ λ λ λ ξ ξ λ λ ξ λ F T F T IC X E X E X E X E x xdF x I x dF x IC

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AMDA-2008-Session 11 - ROBUST STATISTICS OUTLIER RESISTANT...

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