# Bootstrap a statistic

### Dimitri Shvorob (view profile)

15 Apr 2007 (Updated )

(Extension of BOOTSTRP)

bstrapdemo
% BSTRAPDEMO  Demonstration of BSTRAP and BSTATS
% EXAMPLE   : bstrapdemo (Oh, the FEX code metrics..)
% AUTHOR    : Dimitri Shvorob, dimitri.shvorob@vanderbilt.edu, 4/15/07

B = 1000;

% Simple regression
n = 100;
x = rand(n,1);
i = ones(n,1);
a = 3;
b = 5;
y = a + b*x + .5*randn(n,1);

% Bootstrap calculations
disp('A. "fun" with vector output (OLS estimates of regression intercept and slope)')
ls = bstrap(B,1,'olsvector',[y i x]);
disp('Mean and variance estimates, plus two-sided 95% confidence intervals')
[m,v,cil,ciu] = bstats(ls)        %#ok  note: may want to exclude actual-sample value

disp('B. "fun" with structure output (OLS estimates of regression intercept and slope)')
ls = bstrap(B,1,'olsstructure',[y i x]);
disp('Mean and variance estimates, plus two-sided 95% confidence intervals')
[m,v,cil,ciu] = bstats(ls,'b')    %#ok  note: may want to exclude actual-sample value

% Bootstrap distributions of OLS estimates
ab = [ls.b];                      % note: may want to exclude actual-sample value
subplot(3,1,1)
scatter(x,y,2)
title(['Random sample: \ity = ' num2str(a) ' + ' num2str(b) 'x + \epsilon, \rmwhere \itx ~ U\rm[\it0,1\rm]\it,\epsilon ~ N\rm[\it0,1\rm], \iti = 1,..,100']);

subplot(3,1,2)
opt.dx   = .01;
opt.xmin = a - .5;
opt.xmax = a + .5;
opt.xmrk = a;
histf(ab(1,:),opt)
title(['OLS intercept estimate: bootstrap distribution. (True value = \it' num2str(a) '\rm)'])

subplot(3,1,3)
opt.xmrk = b;
opt.xmin = b - .5;
opt.xmax = b + .5;
histf(ab(2,:),opt)
title(['OLS slope estimate: bootstrap distribution. (True value = \it' num2str(b) '\rm)'])

A. "fun" with vector output (OLS estimates of regression intercept and slope)
Mean and variance estimates, plus two-sided 95% confidence intervals

m =

3.1303
4.9428

v =

0.0088
0.0222

cil =

2.9441
4.6464

ciu =

3.3108
5.2397

B. "fun" with structure output (OLS estimates of regression intercept and slope)
Mean and variance estimates, plus two-sided 95% confidence intervals

m =

3.1394
4.9340

v =

0.0085
0.0224

cil =

2.9576
4.6374

ciu =

3.3256
5.2258