### MATLAB >> Bootstrap Confidence Intervals

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

> 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

```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.

Raj
```

```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

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:-----
```

```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)
```

```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.
```