 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

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