Title: Estimation of the boundary of a variable observed with symmetric error
Authors: Jean-Pierre Florens - Toulouse School of Economics (France)
Leopold Simar - Universite Catholique de Louvain (Belgium)
Ingrid Van Keilegom - KU Leuven (Belgium) [presenting]
Abstract: Consider the model $Y = X + \epsilon$ with $X=\tau + Z$, where $\tau$ is an unknown constant (the boundary of $X$), $Z$ is a random variable defined on $R^+$, $\epsilon$ is a symmetric error, and $\epsilon$ and $Z$ are independent. Based on an iid sample of $Y$, we aim at identifying and estimating the boundary $\tau$ when the law of $\epsilon$ is unknown (apart from symmetry) and in particular its variance is unknown, contrary to most papers in the literature. We propose an estimation procedure based on a minimal distance approach and by making use of Laguerre polynomials. Asymptotic results as well as finite sample simulations are shown.