function [gD,NormgD] = CoefConv(W0,Dtab,M,s0,FTtrue)
global lesZ lesY
if nargin<5, FTtrue=0; end
% if FTtrue==0 compute empirical Fourier Transform
% using fname as the error density
%
% if FTtrue~=0 compute Fourier Transform
% of the normalized true density
N = 2^M; % power used for FFT
freq = -(2*(0:N-1)'-N)/N*pi;
% Dmax = max(Dtab);
Dfreq = freq*Dtab; % N x nD
if ~FTtrue
[Re,Im] = FTempiric(Dfreq,lesZ,lesY);
Xk = (Re+i*Im)./feval(['FT' W0],Dfreq,s0^2);
else
Xk = feval(['FT' W0],Dfreq,s0^2);
end;
xj = ifft(Xk,[],1); % N x nD
gD = diag((-1).^(0:N-1))*xj*diag(sqrt(Dtab)); % N x nD normalizedby sqrt(D)
Xk = conj(Xk);
xj = ifft(Xk,[],1);
hD = diag((-1).^(0:N-1))*xj*diag(sqrt(Dtab));
gD = real([hD(end:-1:2,:);gD]); % the FT coefs are real.
if nargout<2, NormgD=nan; return; end;
%%%% After follow extra .... only used for article
if ~isempty(Z)
NormgD = -sum(abs(gD).^2,1); % contrast
else
if ~strmatch('stable',ername), NormgD = nan; return, end;
% we compute the squared bias
switch (ername)
case 'normal'
NormgD = erfc(s0*pi*Dtab)/2/s0/sqrt(pi);
case 'mixgauss'
NormgD = zeros(size(Dtab));
case 'chi2_3'
K = pi*Dtab/sqrt(6);
NormgD = 3*pi/4-6/4*atan(K)-K.*(5+3*K.^2)./(1+K.^2).^2/2;
NormgD = sqrt(6)*NormgD;
case 'unif'
NormgD = 1/3/pi^2/s0^2./Dtab/2;
case 'exprnd'
spD = pi*Dtab;
NormgD = atan(spD)/pi;
case 'symexp'
spD = s0*pi*Dtab/sqrt(2);
NormgD = 1/2/sqrt(2)/s0 - Dtab/2./(1+spD.^2) - atan(spD)/sqrt(2)/pi/s0;
case 'gamma2'
pD = pi*Dtab/sqrt(6);
NormgD = (2*pD.^3-3*pD)/3./(1+pD.^2).^3 +0.5*(atan(1./pD) - pD./(1+pD.^2));
NormgD = NormgD*sqrt(6)/2/pi;
case 'gamma15'
pD = pi*Dtab/sqrt(15/4);
NormgD = 1 - pD./sqrt(1+pD.^2) - pD./(1+pD.^2).^2;
NormgD = NormgD*sqrt(15/4)/2/pi;
case 'gamma25'
pD = pi*Dtab/sqrt(35/4);
NormgD = 2/3 - pD./sqrt(1+pD.^2) + ...
(pD.^3-pD)./(1+pD.^2).^4 + ...
pD.^3./(1+pD.^2).^(3/2)/3;
NormgD = NormgD*sqrt(35/4)/2/pi;
case 'cauchy'
NormgD = exp(-2*pi*Dtab*s0)/s0;
case 'stable14'
pD = pi*Dtab;
NormgD=exp(-2*pD.^0.25).*(2*pD.^0.75+3*pD.^0.5+3*pD.^0.25+1.5)/pi;
case 'stable12'
pD = pi*Dtab;
NormgD=exp(-2*pD.^0.5).*(pD.^0.5+0.5)/pi;
case 'stable34'
pD = pi*Dtab;
NormgD = 0.8465818119e-1*pD.*(...
15.74960994*exp(-2*pD.^(3/4))./pD.^(3/4)+...
4.166824566*gammainc(0.3333333333, 2*pD.^(3/4))./pD);
otherwise
NormgD = nan*zeros(size(Dtab));
end;
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is part of the package EstimHidden devoted to the estimation of
%
% 1/ the density of X in a convolution model where Z=X+noise1 is observed
%
% 2/ the functions b (drift) and s^2 (volatility) in an "errors in variables"
% model where Z and Y are observed and assumed to follow:
% Z=X+noise1 and Y=b(X)+s(X)*noise2.
%
% 3/ the functions b (drift) and s^2 (volatility) in an stochastic
% volatility model where Z is observed and follows:
% Z=X+noise1 and X_{i+1} = b(X_i) + s(X_i)*noise2
%
% in any cases the density of noise1 is known. We consider three cases for
% this density : Gaussian ('normal'), Laplace ('symexp') and log(Chi2)
% ('logchi2)
%
% See function DeconvEstimate.m and examples in files ExampleDensity.m and
% ExampleRegression.m
%
% Authors : F. COMTE and Y. ROZENHOLC
%
%
% For more information, see the following references:
%
% DENSITY DECONVOLUTION
%%%%%%%%%%%%%%%%%%%%%%%
%
% 1/ "Penalized contrast estimator for density deconvolution",
% The Canadian Journal of Statistics, 34, 431-452, 2006.
% b y F . C O M T E , Y . R O Z E N H O L C , and M . - L . T A U P I N
%
% 2/ "Finite sample penalization in adaptive density deconvolution",
% Journal of Statistical Computation and Simulation.
% Available online.
% b y F . C O M T E , Y . R O Z E N H O L C , and M . - L . T A U P I N
%
% 3/ "Adaptive density estimation for general ARCH models",
% Preprint HAL-CNRS : hal-00101417 at http://hal.archives-ouvertes.fr/
% b y F . C O M T E , J. DEDECKER, and M . - L . T A U P I N .
%
% REGRESSION and AUTO-REGRESSION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 4/ "Nonparametric estimation of the regression function in an
% errors-in-variables model",
% Statistica Sinica, 17, n3, 1065-1090, 2007.
% b y F . C O M T E and M . - L . T A U P I N
%
% 5/ "Adaptive estimation of the dynamics of a discrete time stochastic
% volatility model",
% Preprint HAL-CNRS : hal-00170740 at http://hal.archives-ouvertes.fr/
% by F . C O M T E, C. LACOUR, and Y. R O Z E N H O L C .
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Y o u c a n u s e t h i s s o f t w a r e f o r N O N - C O M M E R C I A L U S E O N L Y .
%
% Y o u c a n d i s t r i b u t e t h i s s o f w a r e u n c h a n g e d a n d o n l y u n c h a n g e d , w h i c h i m p l i e s
% i n c l u d i n g a l l f i l e s f o u n d i n t h e f o l d e r c o i n t a i n n i n g t h i s f i l e .
%
% T h i s s o f t w a r e , a n d a n y p a r t o f i t , i s p r o p o s e d f o r N O N - C O M M E R C I A L U S E
% O N L Y .
%
% P l e a s e , c o n t a c t t h e a u t h o r f o r a n d b e f o r e a n y n o n - a c a d e m i c u s e
% o f t h i s s o f t w a r e .
%
% T o r e p r o d u c e t h i s c o d e o r a n y p a r t o f t h i s c o d e i n t h e o r i g i n a l l a n g u a g e
% o r i n a n y o t h e r l a n g u a g e , f o r c o m m e r c i a l u s e , p l e a s e c o n t a c t t h e A u t h o r
%
% F o r a c a d e m i c p u r p o s e , c i t e this package and t h e c o n n e c t e d p a p e r s .
%
% C o r r e s p o n d i n g a u t h o r : Y . R o z e n h o l c , y v e s . r o z e n h o l c @ u n i v - p a r i s 5 . f r
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Examples in files ExampleDensity.m and ExampleRegression.m
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
