st: can't reproduce bootstrap confidence intervals

[Devra Golbe <devra.golbe@hunter.cuny.edu>]

Listers,

In an attempt to better understand the percentile methods (particularly the 
bias-corrected) for bootstrap CIs, I attempted to reproduce them by 
hand.  My results are different from what Stata produces.  Can anyone show 
me my error?

Thanks,
Devra

********
     log:  d:\temp\biascorr1.log
  log type:  text
 opened on:   5 Jun 2002, 15:46:01

. query born
08 May 2002

. use d:\bstrap4a.dta
(bs: xtnbreg serviol omspl*  ddum1 ddum2 ddum3 unionhat totemp loginp 
firstin dat
> )

.
. summ bs1

    Variable |     Obs        Mean   Std. Dev.       Min        Max
-------------+-----------------------------------------------------
         bs1 |     284   -14.43485   6.165848  -30.57345   1.758053

.  bstat bs1

Bootstrap statistics

Variable |   Reps   Observed       Bias   Std. Err.   [95% Conf. Interval]
---------+-------------------------------------------------------------------
     bs1 |    284  -11.73766  -2.697188   6.165848    -23.8744  .3990816  (N)
         |                                           -25.81105 -1.730178  (P)
         |                                           -21.02399  1.758053 (BC)
-----------------------------------------------------------------------------
                              N = normal, P = percentile, BC = bias-corrected

.  scalar define k =r(reps)

.  scalar define se=r(se)

.  disp r(stat)
-11.737661

. count if bs1<r(stat)
  191

. displ r(N)
191

. scalar define n=r(N)

.
.  scalar define z0=invnorm(n/k)

.  scalar define z95=invnorm(.975)

.
.
.  scalar define p1=normprob(2*z0- z95)

.  scalar define p2=normprob(2*z0 + z95)

.
.  scalar list
        p2 =   .9978401
        p1 =  .14318583
       z95 =   1.959964
        z0 =  .44692449
         n =        191
        se =  6.1658478
         k =        284

.
. /*percentile CI*/
.  centile bs1, centile (.025, .975)

                                                       -- Binom. Interp. --
    Variable |     Obs  Percentile      Centile        [95% Conf. Interval]
-------------+-------------------------------------------------------------
         bs1 |     284       .025     -30.57345       -30.57345   -29.28233*
             |               .975     -28.39507       -30.57345   -25.96878*

* Lower (upper) confidence limit held at minimum (maximum) of sample

.
. /*bias corrected CI*/
.  centile bs1, centile (.14318583)

                                                       -- Binom. Interp. --
    Variable |     Obs  Percentile      Centile        [95% Conf. Interval]
-------------+-------------------------------------------------------------
         bs1 |     284     .14319     -30.57345       -30.57345   -28.41841*

* Lower (upper) confidence limit held at minimum (maximum) of sample

.
end of do-file



______________________________________________________________
Devra L. Golbe, Professor
Dept. of Economics
Hunter College  / CUNY
695 Park Ave., NY, NY 10021
voice:  212-772-5408
fax:     212-772-5398 (office)
          208-361-5964 (e-fax)

http://econ.hunter.cuny.edu/faculty/golbe

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