MATLAB >> Bootstrap Confidence Intervals

by Evren Baysal » Mon, 05 Mar 2007 10:22:01 GMT

Hi,

I would like to find our what scaling and variance stabilizing
parameters are used to construct bias-corrected accelerated bootstrap
confidence intervals with the MATLAB function "bootci".

I will be thankful if I can get a reference on how "bootci" chooses
these parameters.

Thanks

Evren

MATLAB >> Bootstrap Confidence Intervals

by Tom Lane » Wed, 07 Mar 2007 01:28:41 GMT


> I would like to find our what scaling and variance stabilizing

Evren, the person who wrote this function used the following reference:

T.J. DiCiccio and B. Efron (1996), "Bootstrap Confidence Intervals",
Statistical Science, 11(3)

-- Tom

Similar Threads

1. Bootstrap confidence interval

Hi,

"bootci" from statistics toolbox can find the confidence interval for
a parameter.

I have an older version of statistics toolbox, which do not have this
command. Is there any other way to find the confidence interval.

Thanks in advance,
Raj

2. bootstrap confidence interval estimate: function with additional parameters - MATLAB

3. bootstrapped 95% confidence ellipse

I need to add a 95% confidence ellipse to an XY scatter plot.
Schwarz's CONFELLIPSE2 code below, submitted to this group in 1998,
will do this, However, I'd like to produce a Bootstrapped confidence
ellipse. I can use BOOTSTRP in the Statistics Toolbox to resample with
replacement and obtain a bootstrap statistic...I'm just unsure WHAT to
bootstrap.

Any suggestions?

Dave



-----BEGIN MATLAB CODE:-----
function [hh,exy] = confellipse2(xy,conf)
%CONFELLIPSE2 Draws a confidence ellipse.
% CONFELLIPSE2(XY,CONF) draws a confidence ellipse on the current axes
%   which is calculated from the n-by-2 matrix XY and encloses the
%   fraction CONF (e.g., 0.95 for a 95% confidence ellipse).
% H = CONFELLIPSE2(...) returns a handle to the line.

% written by Douglas M. Schwarz
%  XXXX@XXXXX.COM 
% last modified: 12 June 1998

n = size(xy,1);
mxy = mean(xy);

numPts = 181;   % The number of points in the ellipse.
th = linspace(0,2*pi,numPts)';


p = 2;  % Dimensionality of the data, 2-D in this case.

k = finv(conf,p,n-p)*p*(n-1)/(n-p);

[pc,score,lat] = princomp(xy);


ab = diag(sqrt(k*lat));
exy = [cos(th),sin(th)]*ab*pc' + repmat(mxy,numPts,1);

% Add ellipse to current plot
h = line(exy(:,1),exy(:,2),'Clipping','off');
if nargout > 0
   hh = h;
end
-----END MATLAB CODE:-----

4. 95% Confidence Intervals for Bivariate Least Squares Regression Line - MATLAB

5. confidence intervals regress

Hi there,

Suppose I have the simple linear model y=b0+b1*x1+b2*x2+e.
I want to estimate b0,b1,b2 and calculate a confidence 
interval for them. Then I want to see how many times the CI 
contains the true parameter. If I was making everything 
right, for 1000 repetitions, that should be approximately 
950 times. But I am getting 1000 times as a result. What 
wrong with my code?

And another question. The formula used for estimating 95% 
CI in the regress function is b0_hat-Za*SE(b0_hat) where 
Za=1.96 right? But nor this formula, nor the more precise 
Za=1.95996398454002 seems to agree exactly (4 decimals) 
with the result given by bint in the regress function. 
Precision is not much of a problem, all I want to know is 
the correct formula.

And what about confidence intervals when I have weighted 
regression (lscov). The formula there uses a t distribution?

n=200;
b0=20;
b1=3;
b2=4;
lam=3;
for rep=1:1000
e=normrnd(0,10,1,n);
x1=exprnd(lam,1,n)';
x2=exprnd(5,1,n)';
X = [ones(size(x1)) x1 x2]; 
y=b0+b1.*x1+b2.*x2+e';
[b_ols bint]=regress(y,X);

cover1(rep)=(bint(1)<b0<bint(4));
cover2(rep)=(bint(2)<b1<bint(5));
cover3(rep)=(bint(3)<b2<bint(6));
end

cover1=sum(cover1)
cover2=sum(cover2)
cover3=sum(cover3)

6. confidence intervals of large matrix - MATLAB

7. Confidence interval for normal data

Hi,

I would like to know if it is possible to put subscript indices to compute confidence intervals, for exemple something like this (which doesn't work):

for k=1:10
[MUHAT(k) SIGMAHAT(k) MUCI(k) SIGMACI(k)]=normfit(x);
end
 
where "x" is a vector of data that changes 10 times according to another loop (which I mention mention here for simplicity).

Thanks a lot for your help.

8. How are the confidence interval calculated in multcompare? - MATLAB