%
% problem 268
% example epage 250 
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; 
clc; 

addpath('../../Code/CSTool');

%n = 25; 
n = 15; 

x = rand(1,n); 
% compute the bootstrapped standard confidence interval (of the mean): 
B = 1000; 
[m] = bootstrp( B, @mean, x ); 
fprintf( 'The bootstrap estimated standard error is given by %10.5f\n', std(m) );

% compute the jackknifed estimate standard confidence interval (of the mean): 
jack = zeros(1,n); % <- store the jackknifed samples 
for ii=1:n
  jack(ii) = mean( x( setdiff(1:n,ii) ) ); 
end

% get the mean of the jackknifed estimates
TJ = mean(jack);  
jackEstStdError = sqrt( ((n-1)/n)*sum( ( jack - TJ ).^2 ) ); 
fprintf( 'The jackknifed estimated standard error is given by %10.5f\n', jackEstStdError ); 

% assume the theoretical estimate of the standard error for the mean
% (when the draws are from the uniform distribution) is sigma/sqrt(n)
% for a uniform distribution [0,1] => sigma = 1/sqrt(12)
tese = (1/sqrt(12))/sqrt(n); 
fprintf( 'The theoretical estimated standard error is given by %10.5f\n', tese );