
QUANTILE STANDARD ERRORName:
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 HerrellDavis 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 MaritzJarrett method, is computed for the variable X and the desired quantile q as follows:
The second method, based on the kernel density, is computed for a variable X and the desired quantile q as follows:
<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.
LET A = 0.20 QUANTILE STANDARD ERROR Y
SET QUANTILE STANDARD ERROR KERNEL DENSITY
SET QUANTILE STANDARD ERROR KERNEL DENSITY
The specific quantile to compute is specified by entering the following command (before the plot command):
where <value> is a number in the interval (0,1) that specifies the desired quantile.
SET QUANTILE METHOD HERRELL DAVIS BOOTSTRAP SAMPLES 500 BOOTSTRAP QUANTILE STANDARD ERROR PLOT Y LET LCL = B025 LET UCL = B975 The bootstrap method can also be applied to quantile estimated using the order statistic method.
Frank Herrell and C. E. Davis, (1982), "A New DistributionFree Quantile Estimator", Biometrika, 69(3), 635640. Hyndman and Fan (November 1996), "Sample Quantiles in Statistical Packages", The American Statistician, Vol. 50, No. 4, pp. 361365.
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  
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Date created: 07/22/2002 