[ot-users] Questions around kernel smoothing

Andolfatto Loïc loic.andolfatto at epfl.ch
Thu Jan 30 16:36:15 CET 2014


Dear OT users,

I'm willing to build a composed distribution modelling the time of the day ( from 0 to 24) and the flow in a drinking water pipe.
With kernel smoothing, I get the following PDF (which fits surprisingly well my dataset).

[cid:image001.jpg at 01CF1DD9.645CDD30]

However, I still have two questions :

1-      How can I measure the 2D goodness of fit to compare to (mostly multi 1D) parametric strategies found in the litterature ? I thought :

a.       Plotting empirical CDF, parametric-built CDF and my Kernel smoothing CDF for several period of the day shows that KS fits better than parametric techniques. But I would prefer to have numerical values for publication purpose.

b.      Comparing mean value, standard deviations and possibly correlation matrices (Spearman, Pearson) can be a solution, but not a very good one as the correlation between variables is complex.



2-      I know the marginal of the time of the day is Uniform(0,24) (lot of measurements with constant time step in between) but I can't see any way to introduce this preliminary knowledge in the model. Even if my current model is close enough to discrete measurement for the its final use, I would have preferred to have it clean with respect to the information I have.

My short knowledge of mathematics may let me ignorant of some powerful OpenTURNS-implemented tricks. If you have any idea, I would be very grateful.
Thank you for your time, kind regards,

Loïc


Dr. Loïc Andolfatto
Scientific collaborator

EPFL - Hydraulic Machines Laboratory
Ecole Polytechnique Fédérale
Av. de Cour 33 Bis
CH-1007 Lausanne

Phone:      +41 (0)21 693-2514
E-mail :     loic.andolfatto at epfl.ch<mailto:loic.andolfatto at epfl.ch>
Site web : http://lmh.epfl.ch/

[http://www.epfl.ch/img/epfl_small.png]





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