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Dataplot Vol 2 Vol 1

WINSORIZED COVARIANCE

Name:
    WINSORIZED COVARIANCE (LET)
Type:
    Let Subcommand
Purpose:
    Compute the Winsorized covariance of a variable.
Description:
    The standard covariance estimate can be heavily influenced by extreme values. The Winsorized covariance compensates for this by setting the tail values equal to a certain percentile value. For example, for a 90% Winsorized covariance, the bottom 5% of the values are set equal to the value corresponding to the 5th percentile while the upper 5% of the values are set equal to the value corresponding to the 95th percentile. Then the standard covariance formula (HELP COVARIANCE for details) is applied.
Syntax:
    LET <par> = WINSORIZED COVARIANCE <y1> <y2>
                                <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                  <y2> is the second response variable;
                  <par> is a parameter where the computed Winsorized covariance is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = WINSORIZED COVARIANCE Y1 Y2
    LET A = WINSORIZED COVARIANCE Y1 Y2 SUBSET TAG > 2
Note:
    The analyst must specify the percentages to Winsorize in each tail. This is done by defining the internal variables P1 (the lower tail) and P2 (the upper tail). For example, to Winsorize 10% of each tail, do the following:

      LET P1 = 10
      LET P2 = 10
      LET A = WINSORIZED COVARIANCE Y1 Y2
Note:
    Support for the Winsorized covariance has been added to the following plots and commands:

      WINSORIZED COVARIANCE PLOT
      BOOTSTRAP WINSORIZED COVARIANCE PLOT
      JACKNIFE WINSORIZED COVARIANCE PLOT
      CROSS TABULATE WINSORIZED COVARIANCE PLOT
      WINSORIZED COVARIANCE INTERACTION STATISTIC PLOT

    In addition, the command

      SET COVARIANCE TYPE WINSOR

    can be used to specify that the command

      LET C = VARIANCE COVARIANCE MATRIX M

    generates Winsorized variances and covariances for a matrix (instead of the standard variances and covariances normally generated).

Default:
    None
Synonyms:
    None
Related Commands:
    WINSORIZE = Winsorize a variable.
    WINSORIZED STANARD DEVIATION = Compute a Winsorized standard deviation.
    WINSORIZED MEAN = Compute a Winsorized mean.
    WINSORIZED VARIANCE = Compute a Winsorized covariance.
    WINSORIZED CORRELATION = Compute a Winsorized correlation.
    VARIANCE = Compute the variance.
    BIWEIGHT MIDVARIANCE = Compute the biweight midvariance.
Applications:
    Robust Data Analysis
Implementation Date:
    7/2002
Program: 
    DIMENSION 20 COLUMNS 
SKIP 25 
COLUMN LIMITS 20 80 
READ AUTO79.DAT Y1 TO Y12 
LET A1 = COVARIANCE Y1 Y2 
LET A2 = WINSORIZED COVARIANCE Y1 Y2

Date created: 7/22/2002
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.