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qreg1

quantile regression estimation

CALLING SEQUENCE

[r] = qreg1(y,x,tau,w,algo,maxit,eps,big,sigma)

PARAMETERS

Input

* y = a (nobs x 1) real vector of endogenous variable

* x = a (nobs x k) real matrix of exogenous variables

* tau = a (q x 1) vector, the values of the quantiles

* w = a vector of the same size as the endoegnous variable, if the user wants to weight differently the observations (default: equal weights)

* algo = a string, the name of the algorithm ('linpro' or 'qreg_solvelp1')

* maxit = a scalar, the maximum number of iterations allowed (default: none)

* eps = a scalar, the tolerance value for convergence (default: sqrt(%eps))

* big = a scalar, the number used to remove the residuals of the wrong sign (default: 1E20)

* sigma = a scalar, < 1, the scaling factor determines how close the corrector step is allowed to come to the boundary of the constraint set in the interior point method

 

Output

* res = a results tlist with

  - res('meth') = 'quantile'

  - res('y') = y data vector

  - res('x') = x data matrix

  - res('tau') = vectores of quantiles to be estimated

  - res('weights') = 0 or a (nobs x 1) vector of observations weights

  - res('nobs') = # observations

  - res('nvar') = # variables

  - res('beta') = (nvar x q) matrix of quantile estimations

DESCRIPTION

Performs quantile regression on matrices.

EXAMPLE

X = grand(100,3,'nor',0,1);
X1 = X(:,1)
X2 = X(:,2)
Y = 12 + 3*X1 + 5*X2 + .2*X(:,3);
tau = [0.05;0.50;0.75;0.95];
r = qreg1(Y,[ones(100,1) X1 X2],tau,0,'linpro',%inf,sqrt(%eps),1E20,0.99995);
// Performs quantile regression on simulated data, with algorithm 'linpro' (needs to have previously installed the toolbox 'quapro') and default qreg values.

AUTHOR

Eric Dubois 2011

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