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Re: Least Absolute Deviation solution of a linear system
From: |
Michael Creel |
Subject: |
Re: Least Absolute Deviation solution of a linear system |
Date: |
Mon, 16 Feb 2009 01:32:30 -0800 (PST) |
Regarding LAD estimation, it is possible to do with linear or nonlinear
models by defining the LAD objective function, and then using simulated
annealing to do minimization. A function for simulated annealing
minimization is part of the Octave Forge optim package. An example of use
for LAD is:
############### beginning of LAD example script
################################
n = 100;
e = randn(n,1);
x = [ones(n,1) randn(n,1)];
theta = ones(2,1);
y = x*theta + e;
printf("OLS fittted coefficients\n");
ols(y,x)
function obj_value = lad_obj(theta, y, x);
e = abs(y - x*theta);
obj_value = mean(e);
endfunction
# samin controls
ub = [2; 2];
lb = [-1; -1];
nt = 3;
ns = 3;
rt = .5;
maxevals = 1e6;
neps = 3;
functol = 1e-12;
paramtol = 1e-6;
verbosity = 1;
minarg = 1;
sacontrol = { lb, ub, nt, ns, rt, maxevals, neps, functol, paramtol,
verbosity, 1};
printf("LAD fittted coefficients\n");
samin("lad_obj", {theta, y, x}, sacontrol);
############### end of LAD example script ################################
Running this results in the output:
octave:6> lad
OLS fittted coefficients
ans =
1.0351
1.0831
LAD fittted coefficients
================================================
SAMIN results
==> Normal convergence <==
Convergence tolerances:
Function: 1.000000e-12
Parameters: 1.000000e-06
Objective function value at minimum: 0.812300
parameter search width
1.073272 0.000000
1.124825 0.000000
================================================
octave:7>
Regards, Michael
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