Estimating a frontier function using a high-order moments method

International audienceFrontier function estimation can be applied in several problems, such as the estimation of the maximal output of a company given a quantity of input, or the estimation of the maximal temperature at a given point on the surface of the Earth. We present here a method to estimate the frontier function of a finite-dimensional sample. The estimator is based on a kernel regression on high order moments, where we assume that the order of the moments goes to infinity while the bandwidth of the kernel goes to zero. We discuss the asymptotics of our estimator and in particular its uniform consistency and pointwise asymptotic normality, when the conditional distribution function decreases at a polynomial rate to zero in a neighbourhood of the frontier. The finite-sample performance of the estimator is illustrated on a simulation study