% file to generate normal data from a regression with only a contact.

% John Rust University of Maryland, November 2011

global data sigmahat resids;

truemu=4;
truesig=1.5;

nobs=1500;
data=truemu+truesig*randn(nobs,1);

sigmahat=std(data);


muhat=mean(data);

resids=data-muhat;

% plot loglikelihood 

mu=(-4:.1:12)';
llf=zeros(size(mu,1),1);
nllf=zeros(size(mu,1),1);
for i=1:size(mu,1);
    
    llf(i)=lln(mu(i));
   nllf(i)=nlln(mu(i));
   
end;

% the functions lln and nlln compute the *negative* of the log-likelihood
% because Matlab's optimization program, fminunc, is for *minimization* of
% functions, not maximization. So to maximize, we minimize the negative of
% the log-likelihood function

llf=-llf; 
nllf=-nllf;

figure(1);
hold on;
plot(mu,llf,'r-','LineWidth',2);
plot(mu,nllf,'b--','LineWidth',2);
title('Plot of Normal Log-Likelihood Function');
xlabel('Mu value');
ylabel('Log Likelihood value');
legend('Parametric loglikelihood','Semi-Parametric Loglikelihood','Location','Best');
hold off;


muhat=mean(data);
mu_pmle=fminunc(@lln,0);
mu_npmle=fminunc(@nlln,0);

fprintf('Sample Mean:                                           %12.9f\n',muhat);
fprintf('Parametric (gaussian) Maximum Likelihood Estimator:    %12.9f\n',mu_pmle);
fprintf('Semi-Parametric Adaptive Maximum Likelihood Estimator: %12.9f\n',mu_npmle);