WINSORIZED COVARIANCE
Name:
WINSORIZED COVARIANCE (LET)
Type:
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:
Synonyms:
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:
Implementation Date:
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.
