Estimation for Hidden Processes: ExampleRegression.m - File Exchange

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Highlights from
Estimation for Hidden Processes

(YX(1:(n-1)) + YX(2:n))*dX'/2... This is part of the package EstimHidden devoted to the estimation of
CoefConv(W0,Dtab,M,s0,FTtrue) if FTtrue==0 compute empirical Fourier Transform
DeconvCtr(wname,D,M,s02) % This is part of the package EstimHidden devoted to the estimation of
DeconvEstimate(Z,W0,s0,Y) % This is part of the package EstimHidden devoted to the estimation of
DeconvOrd(estimate,a) estimate defines an estimate model for the density (and regression) pb
DeconvPen(Wname,s2,Dtab,n) Wname : type of the known noise
DeconvPenCtr(D,wname,s02,M,c)
DeconvSimul(name,n,W0,s0,B,s) Draw random observations for
FTempiric(X,Z,Y) Fourier transform of the empirical data Z
FTlogchi2(X,sigma2) Fourier transform of the log of the square of a N(0,1)
FTnormal(X,sigma2) Fourier transform of the N(0,sigma2)
FTsymexp(X,sigma2) Fourier transform of the symetric exponential
GARCH(n,alpha,beta,stat)
SinCardBasis(D,coef,X)
drift(x,name)
mcgama(x,y,kf) This program is an adaptation (by Yves) from the direct conversion of the
normal(sigma,n,p)
symexp(sigma,n,p)
volatility(x,name)
ExampleDensity.m
ExampleRegression.m
ReadMe.m
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from Estimation for Hidden Processes by Yves Rozenholc
Nonparametric estimation of density, regression or variance functions for hidden processes using mod

ExampleRegression.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%% HIDDEN REGRESSION Examples ("errors in variables" model)
% Observations vector Z
% The second input argument is noise type
% The third input argument is sigma
% The fourth input argument is observations vector Y
%
% the output is a structure with
%   Dgopt : the selected "dimension" for the density g of X
%   gD : the estimate coefficients for g at the selected dimension Dgopt
%   Dlopt : the selected "dimension" for the product l=b.g
%   lD : the estimate coefficients for l=b.g at the selected dimension Dlopt
%   n : length of the observations
%   abs : linspace(quantila(Z,0.05),quantila(Z,0.95),1001) ->(default values)
%   gord : density g estimates associated to abs
%   lord : l=b.g estimates associated to abs
%   bord : b estimates associated to abs
%   vord : (s^2+b^2)*g estimates associated to abs
%   cord : s^2+b^2 estimates associated to abs
%   s2ord : s^2 estimates associated to abs

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Example A-1/ REGRESSION with errors in variables
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% following the second example of Fan & Truong - Annals of Statistics 1993
n = 2000;
name = 'truong';
W0 = 'normal';
s0 = sqrt(3/7)*0.25;
WY = 'normal';
sY = 0.25;

%%%% SIMULATION
Obs = DeconvSimul(name,n,W0,s0,WY,sY);

%%%% ESTIMATION
estimate = DeconvEstimate(Obs.Z,Obs.W0,Obs.s0,Obs.Y);

subplot(2,2,1)
plot(estimate.abs,pdf('norm',estimate.abs,0.5,0.25),'r',estimate.abs,estimate.gord,'b')
title('density g estimate')
legend('true','estimate')

subplot(2,2,2)
plot(estimate.abs,drift(estimate.abs,name),'r',estimate.abs,estimate.bord,'b')
title('b estimate')

subplot(2,2,3)
plot(estimate.abs,drift(estimate.abs,name).^2+volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.cord,'b')
title('b^2+s^2 estimate')

subplot(2,2,4)
plot(estimate.abs,volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.s2ord,'b')
title('s^2 estimate')


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Example A-2/ REGRESSION with errors in variables
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% following the second example of Fan & Truong - Annals of Statistics 1993
n = 2000;
name = 'truong';
W0 = 'symexp';
s0 = sqrt(3/7)*0.25;
WY = 'normal';
sY = 0.25;

%%%% SIMULATION
Obs = DeconvSimul(name,n,W0,s0,WY,sY);

%%%% ESTIMATION
estimate = DeconvEstimate(Obs.Z,Obs.W0,Obs.s0,Obs.Y);

subplot(2,2,1)
plot(estimate.abs,pdf('norm',estimate.abs,0.5,0.25),'r',estimate.abs,estimate.gord,'b')
title('density g estimate')
legend('true','estimate')

subplot(2,2,2)
plot(estimate.abs,drift(estimate.abs,name),'r',estimate.abs,estimate.bord,'b')
title('b estimate')

subplot(2,2,3)
plot(estimate.abs,drift(estimate.abs,name).^2+volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.cord,'b')
title('b^2+s^2 estimate')

subplot(2,2,4)
plot(estimate.abs,volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.s2ord,'b')
title('s^2 estimate')


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Example B-1/ AUTO-REGRESSION with errors in variables
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% following the second example of Fan & Truong - Annals of Statistics 1993
n = 2000;
name = 'M10';
W0 = 'normal';
s0 = 0.1;
WY = 'normal';
sY = 1;

%%%% SIMULATION
Obs = DeconvSimul(name,n,W0,s0,WY,sY);

%%%% ESTIMATION
estimate = DeconvEstimate(Obs.Z,Obs.W0,Obs.s0,Obs.Y);

subplot(2,2,1)
plot(estimate.abs,estimate.gord,'b')
title('density g estimate')

subplot(2,2,2)
plot(estimate.abs,drift(estimate.abs,name),'r',estimate.abs,estimate.bord,'b')
title('b estimate')
legend('true','estimate')

subplot(2,2,3)
plot(estimate.abs,drift(estimate.abs,name).^2+volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.cord,'b')
title('b^2+s^2 estimate')

subplot(2,2,4)
plot(estimate.abs,volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.s2ord,'b')
title('s^2 estimate')


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Example B-2/ AUTO-REGRESSION with errors in variables
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% following the second example of Fan & Truong - Annals of Statistics 1993
n = 2000;
name = 'M11';
W0 = 'symexp';
s0 = 0.1;
WY = 'normal';
sY = 1;

%%%% SIMULATION
Obs = DeconvSimul(name,n,W0,s0,WY,sY);

%%%% ESTIMATION
estimate = DeconvEstimate(Obs.Z,Obs.W0,Obs.s0,Obs.Y);

subplot(2,2,1)
plot(estimate.abs,estimate.gord,'b')
title('density g estimate')

subplot(2,2,2)
plot(estimate.abs,drift(estimate.abs,name),'r',estimate.abs,estimate.bord,'b')
title('b estimate')
legend('true','estimate')

subplot(2,2,3)
plot(estimate.abs,drift(estimate.abs,name).^2+volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.cord,'b')
title('b^2+s^2 estimate')

subplot(2,2,4)
plot(estimate.abs,volatility(estimate.abs,name).^2,'r',estimate.abs,estimate.s2ord,'b')
title('s^2 estimate')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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, yves.rozenholc@univ-paris5.fr
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Examples in files ExampleDensity.m and ExampleRegression.m
%
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Highlights from Estimation for Hidden Processes

Highlights from
Estimation for Hidden Processes