Frontier estimation with kernel regression on high order moments

Stéphane Girard (1) , Armelle Guillou (2) , Gilles Stupfler (2)

1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
2 IRMA - Institut de Recherche Mathématique Avancée

We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on high order moments. It is assumed that the order of the moments goes to infinity while the bandwidth of the kernel goes to zero. The consistency of the estimator is proved under mild conditions on these two parameters. The asymptotic normality is also established when the conditional distribution function decreases at a polynomial rate to zero in the neighborhood of the frontier. The good performance of the estimator is illustrated on some finite sample situations.

Mots clés: Frontier estimation; Kernel estimation; Asymptotic normality

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Stéphane Girard, Armelle Guillou, Gilles Stupfler. Frontier estimation with kernel regression on high order moments. Journal of Multivariate Analysis, 2013, 116, pp.172-189. ⟨10.1016/j.jmva.2012.12.001⟩. ⟨hal-00499369v3⟩