Density estimation by the penalized combinatorial method
Journal of Multivariate Analysis
| Hi-index | 754.84 |
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.