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## Copyright (C) 2007 Michael Creel <michael.creel@uab.es>
##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## kernel_optimal_bandwidth: find optimal bandwith doing leave-one-out cross validation
## inputs:
## * data: data matrix
## * depvar: column vector or empty ("").
## If empty, do kernel density, orherwise, kernel regression
## * kernel (optional, string) the kernel function to use
## output:
## * h: the optimal bandwidth
function bandwidth = kernel_optimal_bandwidth(data, depvar, kernel)
if (nargin < 2) error("kernel_optimal_bandwidth: 3 arguments required"); endif
if (nargin < 3) kernel = "kernel_epanechnikov"; endif
do_density = false;
if isempty(depvar) do_density = true; endif;
# SA controls
ub = 3;
lb = -5;
nt = 1;
ns = 1;
rt = 0.05;
maxevals = 50;
neps = 5;
functol = 1e-2;
paramtol = 1e-3;
verbosity = 0;
minarg = 1;
sa_control = { lb, ub, nt, ns, rt, maxevals, neps, functol, paramtol, verbosity, 1};
# bfgs controls
bfgs_control = {10};
if do_density
bandwidth = samin("kernel_density_cvscore", {1, data, kernel}, sa_control);
bandwidth = bfgsmin("kernel_density_cvscore", {bandwidth, data, kernel}, bfgs_control);
else
bandwidth = samin("kernel_regression_cvscore", {1, data, depvar, kernel}, sa_control);
bandwidth = bfgsmin("kernel_regression_cvscore", {bandwidth, data, depvar, kernel}, bfgs_control);
endif
bandwidth = exp(bandwidth);
endfunction
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