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st: Bootstrap estimate of variance


From   "Doogar, Rajib" <doogar@uiuc.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: Bootstrap estimate of variance
Date   Fri, 17 Aug 2007 11:30:58 -0500

I would appreciate any help with the following issue/questions.

Objective:
Given n (iid ~ N(0,s)) observations on x, I want to test x_i=0, (i, 1..n) (one test for each observation). s is unknown. The n observations come from a "perturbed" environment, raising concerns that the in-sample estimate of variance may not be the correct estimate to use in the test.  Fortunately I also have m observations from a "unperturbed" or "normal" environment available.

Observation:
I could always use the variance of the m observations to estimate s.

Questions:
1. Can I do better by using bootstrap, e.g.:
// estimate variance based on random sample, store estimates in bsvar.dta
bs var=r(Var), reps(R) [size(Z)] [seed(S)] [nodots] saving(bsvar, replace): summ var1
// obtain mean of R estimated variances
use bsvar.dta, clear
summ var

2. In particular, would the mean of "var" reported by the final "summ" command in the sequence above be a legitimate bootstrap estimate of the variance of x during the "normal" periods?

Many thanks,

Rajib Doogar,
Department of Accountancy,
The University of Illinois at Urbana-Champaign
1206 S. Sixth Street, Champaign, IL 61820
Ph: 217.244.8083, Fax: 217.244.0902
http://www.cba.uiuc.edu/doogar




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