
BIWEIGHT MIDCORRELATIONName:
Many statistics have one of these properties. However, it can be difficult to find statistics that are both resistant and have robustness of efficiency. The standard Pearson correlation coefficient is the optimal estimator for Gaussian data. However, it is not resistant and it does not have robustness of efficiency. The Spearman rank correlation is one example of a robust estimate of correlation. The biweight midcorrelation estimator is another alternative correlation estimate. It is both resistant and robust of efficiency. The biweight midcorrelation can be defined in terms of the biweight midvariance and the biweight midcovariance:
where \( s_{bxy} \) is the biweight midcovariance between X and Y and \( s_{bxx} \) and \( s_{byy} \) are the biweight midvariances of X and Y, respectively.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the computed biweight midcorrelation is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = BIWEIGHT MIDCORRELATION Y1 Y2 SUBSET TAG > 2
can be used to specify an alternate correlation measure to compute in the CORRELATION MATRIX command. The following types are supported:
Mosteller and Tukey (1977), "Data Analysis and Regression: A Second Course in Statistics," AddisonWesley, pp. 203209.
SKIP 25 READ MATRIX IRIS.DAT Y1 Y2 Y3 Y4 X LET M = CREATE MATRIX Y1 Y2 Y3 Y4 SET CORRELATION TYPE BIWEIGHT LET B = CORRELATION MATRIX Y1 Y2 Y3 Y4Program 2: SKIP 25 READ IRIS.DAT Y1 Y2 Y3 Y4 X . MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT 2 1 BOOTSTRAP SAMPLES 500 BOOTSTRAP BIWEIGHT MIDCORRELATION PLOT Y1 Y2 X1LABEL B025 = ^B025, B975=^B975 HISTOGRAM YPLOT END OF MULTIPLOT MOVE 50 96 JUSTIFICATION CENTER TEXT BIWEIGHT MIDCORRELATION BOOTSTRAP: IRIS DATA
 
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Date created: 07/22/2002 