112 lines
3.4 KiB
Matlab
112 lines
3.4 KiB
Matlab
function dy = prodmom_deriv(V,ii,nu,dV,dC)
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% This function builds upon and extends prodmom.m to compute the
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% derivatives of product moments of normally distributed variables with
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% respect to standard errors and correlation parameters.
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% prodmom.m is part of replication codes of the following paper:
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% Kan, R.: "From moments of sum to moments of product." Journal of
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% Multivariate Analysis, 2008, vol. 99, issue 3, pages 542-554.
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% =========================================================================
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% Copyright (C) 2019-2020 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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% =========================================================================
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if nargin<3
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nu = ones(size(ii));
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end
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s = sum(nu);
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if s==0
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dy = zeros(1,1,size(dV,3));
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return
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end
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if rem(s,2)==1
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dy = zeros(1,1,size(dV,3));
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return
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end
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nuz = nu==0;
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nu(nuz) = [];
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ii(nuz) = [];
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m = length(ii);
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V = V(ii,ii);
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dV = dV(ii,ii,:);
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s2 = s/2;
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%
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% Use univariate normal results
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%
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if m==1
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dy = s2*V^(s2-1)*dV*prod([1:2:s-1]);
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dy = reshape(dy,1,size(dV,3));
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return
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end
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%
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% Use bivariate normal results when there are only two distinct indices
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%
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if m==2
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rho = V(1,2)/sqrt(V(1,1)*V(2,2));
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drho = dC(ii(1),ii(2),:);
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[tmp,dtmp] = bivmom(nu,rho);
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dy = (nu(1)/2)*V(1,1)^(nu(1)/2-1)*dV(1,1,:) * V(2,2)^(nu(2)/2) * tmp...
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+ V(1,1)^(nu(1)/2) * (nu(2)/2)*V(2,2)^(nu(2)/2-1)*dV(2,2,:) * tmp...
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+ V(1,1)^(nu(1)/2) * V(2,2)^(nu(2)/2) * dtmp * drho;
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dy = reshape(dy,1,size(dV,3));
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return
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end
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%
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% Regular case
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%
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[nu,inu] = sort(nu,2,'descend');
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V = V(inu,inu); % Extract only the relevant part of V
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dV = dV(inu,inu,:); % Extract only the relevant part of dV
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x = zeros(1,m);
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V = V./2;
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dV = dV./2;
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nu2 = nu./2;
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p = 2;
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q = nu2*V*nu2';
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%dq = nu2*dV*nu2';
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%dq = multiprod(multiprod(nu2,dV),nu2');
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dq = NaN(size(q,1), size(q,2), size(dV,3));
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for jp = 1:size(dV,3)
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dq(:,:,jp) = nu2*dV(:,:,jp)*nu2';
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end
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dy = 0;
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for i=1:fix(prod(nu+1)/2)
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dy = dy+p*s2*q^(s2-1)*dq;
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for j=1:m
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if x(j)<nu(j)
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x(j) = x(j)+1;
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p = -round(p*(nu(j)+1-x(j))/x(j));
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%dq = dq-2*(nu2-x)*dV(:,j,:)-dV(j,j,:);
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%dq = dq-2*multiprod((nu2-x),dV(:,j,:))-dV(j,j,:);
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for jp=1:size(dV,3)
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dq(:,:,jp) = dq(:,:,jp)-2*(nu2-x)*dV(:,j,jp)-dV(j,j,jp);
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end
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q = q-2*(nu2-x)*V(:,j)-V(j,j);
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break
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else
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x(j) = 0;
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if rem(nu(j),2)==1
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p = -p;
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end
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%dq = dq+2*nu(j)*multiprod((nu2-x),dV(:,j,:))-nu(j)^2*dV(j,j,:);
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for jp=1:size(dV,3)
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dq(:,:,jp) = dq(:,:,jp)+2*nu(j)*(nu2-x)*dV(:,j,jp)-nu(j)^2*dV(j,j,jp);
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end
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q = q+2*nu(j)*(nu2-x)*V(:,j)-nu(j)^2*V(j,j);
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end
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end
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end
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dy = dy/prod([1:s2]);
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dy = reshape(dy,1,size(dV,3)); |