Asymptotic normality of the L1-error of a boundary estimator
Résumé
We present a result on the asymptotic normality of the $L_1$-error of the sup-piecewise constant estimator of frontier functions. This result is obtained by means of an original squeezing method of the empirical point process between two Poisson point processes. The result is available under the best rate of convergence, but becomes fully useful under sub-optimal conditions.