DeconvSimul(name,n,W0,s0,B,s)

function [Obs,isautoregressive,X] = DeconvSimul(name,n,W0,s0,B,s)

densitycase = (nargin<5);
if nargin<6, s=[]; end

% Draw random observations for 
%
%   density deconvolution with observations Z=X+s0.e0 where X i.i.d f
% or 
%   regression with errors in variable with
%   observations Z=X+s0.e0 with X i.i.d. f and Y=b(X)+s(X).e
% or 
%   autoregression with errors in variable with
%   observations Z=X+s0.e0 with X satisfies X[i+1]=b(X[i])+s(X[i]).e[i+1]
%
% name = model name
% n = sample size
% W0 = type of convolution noise e0 (known)
% s0 = standard deviation of convolution noise e0 (known)
% B = type of regression noise e (unknown)
% s = standard deviation of regression noise e (unknown) 
%   (if s is missing use default values of previous papers)
%
% The model is assumed to be a density convolution model 
% if only 4 parameters are given to the function
%
% Return
% Z the density observations
% Y the regression observations 
% and
% (u,v) the coordinates of 
%       the true f (density deconvolution case)
%       or
%       the true b (regression case)
% (u,w) the coordinates of the true s (regression case)
%
% W0 the noise type to use for estimation (usefull only to test
% misspecification of noise type)

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% the unobservable X
if densitycase % ONLY for DENSITY CASES
    if strmatch('dependent',name) 
        % special case for dependent data
        X = feval(name(1:10),str2num(name(12:end)),n);
        switch (name(1:10))
            case 'dependent1'
                name='normal';
            case 'dependent2'
                name='mixgauss';
        end;
    elseif strmatch('GARCH',name)
        % W0 is alpha
        % s0 is beta
        X = GARCH(n,W0,s0,2000);
    else
        % general density case
        X = feval(name,1,n,1); 
    end;
    isautoregressive = 0;
else % ONLY for REGRESSION and AUTO-REGRESSION CASES
    [X,isautoregressive] = RegressionAbs(name,n,s); % UNOBSERVABLE
end; 

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% the OBSERVABLE noisy Z
if strmatch('Wmix',W0)
  e0 = Wmix(1,length(X),1,str2num(W0(7:end)));
  switch(W0(5))
    case '1'
      W0 = 'symexp';
    case '2'
      W0 = 'normal';
  end;
else
  e0 = feval(W0(1:6),1,length(X)); 
end;

Z = X + s0*e0;

Obs.isauto = nan;
Obs.Z = Z;
Obs.W0 = W0;
Obs.s0 = s0;
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if densitycase, Obs.Y=nan; return, end; % STOP because density case 


% REGRESSION CASE
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% the noisy Y
if isautoregressive
    Obs.Y = Z(2:end);
    Obs.Z = Z(1:end-1);
    X = X(1:end-1);
    Obs.isauto = 1;
else
    if strmatch('Wmix',B)
      e = Wmix(1,length(X),1,str2num(B(7:end)));
      switch(B(5))
        case '1'
          B = 'symexp'
        case '2'
          B = 'normal'
      end;
    else
      e = feval(B,1,length(X));
    end;
    Obs.Y = drift(X,name) + s*volatility(X,name).*e; % OBSERVABLE constructed on the UNOBSERVABLE
                            % s=1 as volatility use already default values
    Obs.isauto = 0;
end
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function [X,isautoregressive] = RegressionAbs(name,n,s)

if nargin<3, s=[]; end

% Return 
%   the abscissa of the 'regression with errors in variable' model
% or
%   the autoregressive trajectory 

isautoregressive = 0;

switch(name)
    case {'fan','truong'}
        X = 0.25*randn(n,1)+0.5;
    case {'RM9','RM10','RM11'}
        X = 4*rand(n,1)-2;
    otherwise % AUTOREGRESSIVE MODELS
        isautoregressive = 1;
        X = zeros(1001+n,1);
        N = randn(size(X));
        for i=1:n+1000
        	X(i+1)=drift(X(i),name)+s*volatility(X(i),name)*N(i);
        end
        X = X(1001: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.
%    by F. COMTE, Y. ROZENHOLC, and M.-L. TAUPIN
%
% 2/ "Finite sample  penalization in adaptive density deconvolution", 
%    Journal of Statistical Computation and Simulation. 
%    Available online.
%    by F. COMTE, Y. ROZENHOLC, and M.-L. TAUPIN
%
% 3/ "Adaptive density estimation for general ARCH models", 
%    Preprint HAL-CNRS : hal-00101417  at http://hal.archives-ouvertes.fr/
%    by F. COMTE, J. DEDECKER, and  M.-L. TAUPIN. 
%
% REGRESSION and AUTO-REGRESSION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 4/ "Nonparametric estimation of the regression function in an
%    errors-in-variables model", 
%    Statistica Sinica, 17, n3, 1065-1090, 2007. 
%    by F. COMTE and M.-L. TAUPIN
%
% 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. COMTE, C. LACOUR, and Y. ROZENHOLC. 
%
%
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%
% You can use this software for NON-COMMERCIAL USE ONLY. 
%
% You can distribute this sofware unchanged and only unchanged, which implies
% including all files found in the folder cointainning this file.
%
% This software, and any part of it, is proposed for NON-COMMERCIAL USE 
% ONLY. 
%
% Please, contact the author for and before any non-academic use
% of this software.
%
% To reproduce this code or any part of this code in the original language 
% or in any other language, for commercial use, please contact the Author
%
% For academic purpose, cite this package and the connected papers.
%
% Corresponding author : Y. Rozenholc, [e-mail]
%
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%
% Examples in files ExampleDensity.m and ExampleRegression.m
%
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