% bs_ex2.m: Bootstrap example for PCA
%
% from pp. 61-70 of Efron & Tibshirani
% RTB 5/31/02

% NOTE: For compatibility with different web browsers,
% this file has been renamed 'poissonTutorial.txt'. In
% order to use it in MATLAB, you should rename it as
% 'poissonTutorial.m' and then open it up with the 
% MATLAB editor.

% do 200 iterations of the bootstrap
nboot = 200;

% load test score data from Mardia et al. 1979; p. 62
load bs_data.txt;
X = bs_data;

% calculate the observed value
[PC,SCORE,LATENT,TSQUARE] = princomp(X);
th = LATENT(1) / sum(LATENT);

% calculate the standard error of the variance estimate
TH = bootstrp(nboot, 'pca', X);
std(TH);

% 95% CI
myalpha = 0.05;
ci = std(TH) * norminv(1-myalpha/2);
thHi = th + ci
thLo = th - ci