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kernel_optimal_bandwidth.m

# 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 2 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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