QUANTILE STANDARD ERROR
Name:
QUANTILE STANDARD ERROR (LET)
Type:
Purpose:
Compute the standard error for a user specified quantile for
a variable.
Description:
The qth quantile of a data set is defined as that value
where a q fraction of the data is below that value and (1-q)
fraction of the data is above that value. For example, the
0.5 quantile is the median.
Dataplot supports two methods for computing the quantile.
The first method is the conventional method based on the order
statistic. The second method, called the Herrell-Davis method,
is based on using all the order statistics. The standard error
methods given here only apply to the first method.
Two methods for obtaining the standard errors for the quantiles
are supported.
The first method, called the Maritz-Jarrett method, is computed
for the variable X and the desired quantile q as
follows:
- Sort the X in ascending order.
- Let m = [q*n + 0.5] (i.e., round
down to the nearest integer).
- A = m - 1
- B = n - m
- Wi =
BETCDF(i/n,A,B) -
BETCDF((i-1)/n,A,B)
where BETCDF is the beta cumulative distribution
function with shape parameters A and B.
The second method, based on the kernel density, is computed for
a variable X and the desired quantile q as follows:
- Let
where
is the estimated quantile.
- Compute the number of observations of X
contained in the interval X +/- h.
Call this NINT.
- The standard error of
Syntax:
LET <par> = <quant> QUANTILE STANDARD ERROR
<y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<qaunt> is a number or parameter in the range (0,1)
that specifies the desired quantile;
<par> is a parameter where the computed quantile
standard error is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
SET QUANTILE STANDARD ERROR MARITZ-JARRETT
LET A = 0.20 QUANTILE STANDARD ERROR Y
SET QUANTILE STANDARD ERROR KERNEL DENSITY
LET XQ = 0.20
LET A = XQ QUANTILE STANDARD ERROR Y
SET QUANTILE STANDARD ERROR KERNEL DENSITY
LET XQ = 0.20
LET A = XQ QUANTILE STANDARD ERROR Y SUBSET TAG > 1
Note:
The following command is used to determine which method
is used to compute the quantile standard error:
SET QUANTILE STANDARD ERROR
<KERNEL DENSITY/MARITZ JARRETT>
Note:
Support for the quantile standard error has been added to the
following plots:
QUANTILE STANDARD ERROR PLOT
CROSS TABULATE QUANTILE STANDARD ERROR PLOT
BOOTSTRAP QUANTILE STANDARD ERROR PLOT
JACKNIFE QUANTILE STANDARD ERROR PLOT
DEX QUANTILE STANDARD ERROR PLOT
QUANTILE STANDARD ERROR INFLUENCE CURVE
INTERACTION QUANTILE STANDARD ERROR PLOT
The specific quantile for which the standard error is to be
computed is specified by entering the following command (before
the plot command):
where is a number in the interval (0,1) that specifies
the desired quantile.
Note:
Default:
The default is to use the Maritz-Jarrett method to
compute the quantile standard error.
Synonyms:
Related Commands:
QUANTILE
|
= Compute a quantile of a variable.
|
MEDIAN
|
= Compute the median of a variable.
|
LOWER QUARTILE
|
= Compute the lower quartile of a variable.
|
UPPER QUARTILE
|
= Compute the upper quartile of a variable.
|
FIRST DECILE
|
= Compute the first decile (the 10th quantile) of
a variable.
|
STATISTIC PLOT
|
= Generate a statistic versus subset plot for
a given statistic.
|
CROSS TABULATE PLOT
|
= Generate a statistic versus subset plot (two
group variables) for a given statistics.
|
BOOTSTRAP PLOT
|
= Generate a bootstrap plot for a given statistic.
|
INFLUENCE CURVE
|
= Generate an influence curve for a given statistic.
|
DEX PLOT
|
= Generate a dex plot for a given statistic.
|
INTERACTION STATISTIC PLOT
|
= Generate an interaction plot for a given statistic.
|
Reference:
"Introduction to Robust Estimation and Hypothesis Testing",
Rand Wilcox, Academic Press, 1997.
Applications:
Implementation Date:
Program:
LET Y1 = NORMAL RANDOM NUMBERS FOR I = 1 1 100
LET XQ = 0.05
LET P05 = XQ QUANTILE Y1
LET P05SE = XQ QUANTILE STANDARD ERROR Y1
Date created: 7/22/2002
Last updated: 4/4/2003
Please email comments on this WWW page to
alan.heckert@nist.gov.
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