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test_trivial_estimation.m

 % Copyright (c) 2008 the authors listed at the following URL, and/or
 % the authors of referenced articles or incorporated external code:
 % http://en.literateprograms.org/Matlab_regressions?action=history&offset=20080704101939
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 % Retrieved from: http://en.literateprograms.org/Matlab_regressions?oldid=13869
 
 
 f  = @(a,x)(a*x./(1+a*x))
 a  = sqrt(2)
 s  = .05;
 x  = (0:.1:10)';
 
 y  = f(a,x);
 ny = y + randn(size(y))*s;
 
 figure('Color',[0.9412 0.9412 0.9412 ]);
 h1 = subplot(1,2,1);
 plot(x,y,'-b',x,ny,'.k','linewidth',2);
 
 
 g  = @(x,y)(y./(x-x.*y))
 
 ai = g(x,ny);
 
 h2 = subplot(1,2,2);
 boxplot(ai);
 
 
 ah = mean(ai(~isinf(ai)));
 
 title(sprintf('$\\hat a$ = %5.5f ; real a = %5.5f', ah, a), 'interpreter', 'latex');

 
 axes(h1);
 hold on
 plot(x, f(ah, x), ':r', 'linewidth', 2);
 hold off
 legend({'theoretical', 'observed', 'estimation'});