Kernel Density Estimation and Goodness-of-Fit Test in Adaptive Tracking

Authors:
Bernard Bercu;Bruno Portier
Affiliations:
Bernard.Bercu@math.u-bordeaux1.fr;Bruno.Portier@insa-rouen.fr
Venue:
SIAM Journal on Control and Optimization
Year:
2008

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Brief paper: A new concept of strong controllability via the Schur complement for ARX models in adaptive tracking

Automatica (Journal of IFAC)

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Abstract

We investigate the asymptotic properties of a recursive kernel density estimator of the driven noise of multivariate ARMAX models in adaptive tracking. We provide an almost sure pointwise and uniform strong law of large numbers as well as a pointwise and multivariate central limit theorem. We also carry out a goodness-of-fit test together with some simulation experiments.