
INFLUENCE CURVEName:
Given a set of univariate data points, Y, and a specified statistic, the influence is studied by determining how the value of the statistic changes as a single point is added to Y. Specifically, we define a set of X values (typically over a fairly broad range relative to the original Y values). The influence curve is generated by plotting the value of the computed statistic with a single point of X added to Y against that X value. Several features are of interest in the influence curve:
where <stat> is one of the following statistics: MEAN, MIDMEAN, MEDIAN, TRIMMED MEAN, WINDSORIZED MEAN, BIWEIGHT LOCATION, HODGESLEHMAN, GEOMETRIC MEAN, HARMONIC MEAN, STANDARD DEVIATION, RELATIVE STANDARD DEVIATION, STANDARD DEVIATION OF MEAN, TRIMMED MEAN STANDARD ERROR, RELATIVE VARIANCE (or COEFFICIENT OF VARIATION), VARIANCE, VARIANCE OF THE MEAN, RANGE, GEOMETRIC STANDARD DEVIATION, AVERAGE ABSOLUTE DEVIATION (or AAD), MEDIAN ABSOLUTE DEVIATION (or MAD), INTERQUARTILE RANGE, PERCENTAGE BEND MIDVARIANCE, BIWEIGHT SCALE, BIWEIGHT MIDVARIANCE, WINSORIZED VARIANCE, WINSORIZED STANDARD DEVIATION, MIDRANGE, MAXIMUM, MINIMUM, EXTREME, SKEWNESS, KURTOSIS, AUTOCORRELATION, AUTOCOVARIANCE, LOWER HINGE, UPPER HINGE, LOWER QUARTILE, UPPER QUARTILE, <FIRST/SECOND/THIRD/FOURTH/FIFTH/SIXTH/ SEVENTH/EIGHTH/NINTH/TENTH> DECILE, PERCENTILE, QUANTILE, QUANTILE STANDARD ERROR, NORMAL PPCC, SINE FREQUENCY, SINE AMPLITUDE, CP, CPK, CNPK, CPM, CC, CPL, CPU, EXPECTED LOSS, PERCENT DEFECTIVE, TAGUCHI SN0 (or SN), TAGUCHI SN+ (or SNL), TAGUCHI SN (or SNS), TAGUCHI SN00 (or SN2); <y> is the response (= dependent) variable; <x> is a variable containing a sequence of X values; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
BIWEIGHT LOCATION INFLUENCE CURVE Y X1
LET Y = NORMAL RANDOM NUMBERS FOR I = 1 1 30 LET XSEQ = SEQUENCE 10 0.1 10 LET N = SIZE XSEQ LET NY = SIZE Y LET NTEMP = NY1 + 1 LOOP FOR K = 1 1 N LET XTEMP = XSEQ(K) LET Y(NTEMP) = XTEMP LET A = MEAN Y LET YNEW(K) = A END OF LOOP PLOT YNEW XTEMPThis basic idea can be easily adapted to unsupported statistics. Default:
Rand Wilcox (1997). "Introduction to Robust Estimation and Hypothesis Testing", Academic Press.
LET XSEQ = SEQUENCE 20 0.1 20 . MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 100 MULTIPLOT SCALE FACTOR 2 . TITLE MEAN INFLUENCE CURVE MEAN INFLUENCE CURVE Y XSEQ LET P1 = 10 LET P2 = 10 TITLE TRIMMED MEAN INFLUENCE CURVE TRIMMED MEAN INFLUENCE CURVE Y XSEQ TITLE WINSORIZED MEAN INFLUENCE CURVE WINSORIZED MEAN INFLUENCE CURVE Y XSEQ TITLE BIWEIGHT LOCATION INFLUENCE CURVE BIWEIGHT LOCATION INFLUENCE CURVE Y XSEQ . END OF MULTIPLOT
 
Date created: 07/18/2002 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 