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st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-


From   "Vasyl Druchkiv" <dvv1985@yahoo.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-
Date   Mon, 12 Nov 2012 22:32:10 +0100

Dear statisticians,

I try to estimate CI's for the median with -bpmedian- or with -bootstrap-
using 

*--------------------- begin example ------------------
centile var
bootstrap median=r(p50): sum var, detail
*--------------------- end example --------------------

The problem is that I get empty cells on standard error and confidence
intervals either by implementing -bpmediam- or -bootstrap-. 

*--------------------- begin example ------------------
Bonett-Price confidence interval for median of: var
Number of observations: 16872
----------------------------------------------------------------------------
--
       var |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+--------------------------------------------------------------
--
       _cons |        -.8          .        .       .            .
.
*--------------------- end example ------------------


I looked for the calculation method used in -bpmedian- . This method is
described in:
    Bonett, D. G. and Price, R. M.  2002.  Statistical inference for a
linear function of medians:  Confidence
    intervals, hypothesis testing, and sample size requirements.
Psychological Methods 7(3): 370-383.

Furthermore, I tried  to estimate CI's with SPSS using bootstrap and got
(-0.8;-0.8) for 95% CI's. It means that the problem occurs when both limits
coincide with the median. However, the method described in Bonnett-Price
uses the formula:
sum(cjηj)±Za/2(sum(cj2varηj))^1/2  (pp: 372)
So, even if the last term is equal to 0 due to the pointy distribution  (var
ηj=0), lower and upper limits must be displayed in stata output and be equal
to -0.8 in my example. Can I just assume that CI's are  equal to median?

Thank you,
Vasyl Druchkiv



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