Minimum empirical square error estimator
The code solves this question :
Consider the following probability density function on hx; yi. f (x) = Uniform[-2; 2] and f (y|x) = N(u,sigma^2) where u=0.3x^3-0.6x^2+0.05x-3 and sigma =0.25 Generate 20 i.i.d samples from this distribution. Now find the minimum empirical square error estimator from the class of all 3rd degree polynomials. Do the same for the class of all 5th degree polynomials. Plot the data superimposed with the two polynomials. Report the polynomials and the error in both cases.