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Unformatted text preview: ROBUST STATISTICS OUTLIER RESISTANT METHODS 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. 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. BoxPlot Consider univariate data. We can compute the five number summary of the data (Min, Q , Median, Q , Max). 0.98 0.99 1.00 1.01 1.02 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 F T, = = + = 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 , } { , =  = = + = + = = =   F T F T IC X E X E X E X E x xdF x I x dF x IC Influence Function of the Median...
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This note was uploaded on 05/07/2009 for the course FIN AMDA taught by Professor Proflaha during the Spring '09 term at Indian Institute Of Management, Ahmedabad.
 Spring '09
 ProfLaha

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