Quantile Regression

USAGE: [p,stats]=quantreg(x,y,tau[,order,nboot]);

INPUTS:
x,y: data that is fitted. (x and y should be columns)
Note: that if x is a matrix with several columns then multiple
linear regression is used and the "order" argument is not used.
tau: quantile used in regression.
order: polynomial order. (default=1)
nboot: number of bootstrap surrogates used in statistical inference.(default=200)

stats is a structure with the following fields:
.pse: standard error on p. (not independent)
.pboot: the bootstrapped polynomial coefficients.
.yfitci: 95% confidence interval on polyval(p,x)


Note: uses bootstrap on residuals for statistical inference. (see help bootstrp)
check also: http://www.econ.uiuc.edu/~roger/research/intro/rq.pdf

EXAMPLE:
x=(1:1000)';
y=randn(size(x)).*(1+x/300)+(x/300).^2;
[p,stats]=quantreg(x,y,.9,2);
plot(x,y,x,polyval(p,x),x,stats.yfitci,'k:')
legend('data','2nd order 90th percentile fit','95% confidence interval','location','best')

For references on the method check e.g. and refs therein:
http://www.econ.uiuc.edu/~roger/research/rq/QRJEP.pdf

Copyright (C) 2008, Aslak Grinsted