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A note on density model size testing

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2 Author(s)
Biau, G. ; Lab. de Statistique Theor. et Appliquee, Univ. Pierre et Marie Curie-Paris, Paris, France ; Devroye, L.

Let (Fk)k≥1 be a nested family of parametric classes of densities with finite Vapnik-Chervonenkis dimension. Let f be a probability density belonging to Fk*, where k* is the unknown smallest integer such that f∈Fk. Given a random sample X1,...,Xn drawn from f, an integer k0≥1 and a real number α∈(0,1), we introduce a new, simple, explicit α-level consistent testing procedure of the hypothesis {H0:k*=k0} versus the alternative {H1:k*≠k0}. Our method is inspired by the combinatorial tools developed in Devroye and Lugosi and it includes a wide range of density models, such as mixture models, neural networks, or exponential families.

Published in:

Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 3 )

Date of Publication:

March 2004

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