
PERCENTAGE BEND CORRELATIONName:
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 Pearson correlation coefficient is an optimal estimator for Gaussian data. However, it is not resistant and it does not have robustness of efficiency. The percentage bend correlation estimator, discussed in Shoemaker and Hettmansperger and also by Wilcox, is both resistant and robust of efficiency. The rationale and derivation for this estimate is given in these references. The percentage bend correlation between two variables X and Y is computed as follows:
The value of \( \beta \) is selected between 0 and 0.5. Higher values of \( \beta \) result in a higher breakdown point at the expense of lower efficiency.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the computed percentage bend correlation is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = PERCENTAGE BEND CORRELATION Y1 Y2 SUBSET TAG > 2
where <value> is greater than 0 and less than or equal to 0.5. The default value for \( \beta \) is 0.1.
Rand Wilcox (1997), "Introduction to Robust Estimation and Hypothesis Testing", Academic Press. 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 PERCENTAGE BEND 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 SCALE FACTOR 2 MULTIPLOT 2 1 BOOTSTRAP SAMPLES 500 BOOTSTRAP PERCENTAGE BEND CORRELATION PLOT Y1 Y2 X1LABEL DISPLACEMENT 12 X1LABEL B025 = ^B025, B975=^B975 HISTOGRAM YPLOT END OF MULTIPLOT MOVE 50 96 JUSTIFICATION CENTER TEXT PERCENTAGE BEND CORRELATION BOOTSTRAP: IRIS DATA
 
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Date created: 08/12/2002 