Frontier estimation with local polynomials and high power-transformed data

Stéphane Girard (1) , Pierre Jacob (2)

1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We present a new method for estimating the frontier of a sample. The estimator is based on a local polynomial regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the bandwidth goes to zero. We give conditions on these two parameters for obtaining almost complete convergence. The asymptotic conditional bias and variance of the estimator are provided and its good performance is illustrated for some finite sample situations.

Mots clés: Local polynomials estimator; Power transform; Frontier estimation

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

Stéphane Girard, Pierre Jacob. Frontier estimation with local polynomials and high power-transformed data. Journal of Multivariate Analysis, 2009, 100 (8), pp.1691-1705. ⟨10.1016/j.jmva.2009.01.011⟩. ⟨hal-00384731⟩