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test_trivial_estimation.m

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 3 % (http://creativecommons.org/publicdomain/zero/1.0/).
 4 % 
 5 % THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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11 % SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
12 % 
13 % Retrieved from: http://en.literateprograms.org/Matlab_regressions?oldid=19174
14 
15 
16 f  = @(a,x)(a*x./(1+a*x))
17 a  = sqrt(2)
18 s  = .05;
19 x  = (0:.1:10)';
20 
21 y  = f(a,x);
22 ny = y + randn(size(y))*s;
23 
24 figure('Color',[0.9412 0.9412 0.9412 ]);
25 h1 = subplot(1,2,1);
26 plot(x,y,'-b',x,ny,'.k','linewidth',2);
27 
28 
29 g  = @(x,y)(y./(x-x.*y))
30 
31 ai = g(x,ny);
32 
33 h2 = subplot(1,2,2);
34 boxplot(ai);
35 
36 ah = mean(ai(~isinf(ai)));
37 
38 title(sprintf('$\\hat a$ = %5.5f ; real a = %5.5f', ah, a), 'interpreter', 'latex');
39 
40 axes(h1);
41 hold on
42 plot(x, f(ah, x), ':r', 'linewidth', 2);
43 hold off
44 legend({'theoretical', 'observed', 'estimation'});


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