Regression estimation
We consider a fixed design regression model Y = s(X) + n and want to estimate the unknown function s by a piecewise polynomial computed with an automatic choice of the knots of the subdivision and of the degrees of the polynomials on each sub-interval. This goal is achieved by a penalized least square estimator computed by dynamic programming.
FY3P: Matlab toolbox developed for Comte, Rozenholc (2002) and Comte, Rozenholc (2004). Please cite this last paper when you use this toolbox for academic purpose.
%%% Motorcycle data are located in the FY3P folder
%%% see Silverman (1985) for more details.
> load Motorcycle.data
> sigma2 = var(Motorcycle(:,2))
> plot(Motorcycle(:,1), Motorcycle(:,2),’+’)
> hold on
> initFY3P(‘polynomial’)
> Yd = FY3P(Motorcycle(:,2), sigma2,10,10, Motorcycle(:,1))
> plot(Motorcycle(:,1), Yd, ‘b’)
>
> Yd = FY3P(Motorcycle(:,2), sigma2/2,10,10, Motorcycle(:,1))
> plot(Motorcycle(:,1), Yd, ‘g’)
> hold off
Keywords: regression, model selection, penalized minimum least square estimator, piecewise polynomial, dynamic programming.
Illustration of the FY3P algorithm on the Motorbike data. Tthe signal shows a strong heteroscedastic. Two choices for the unknown variance are used: empirical variance or half of it.
A comparison on the motorbike data of the FY3P algorithm and wavelet analysis provided in Amato, Antoniadis and Pensky (2006)
