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B0766
Title: Estimation of the boundary of a variable observed with symmetric error Authors:  Jean-Pierre Florens - Toulouse School of Economics (France) [presenting]
Abstract: Let $X^*$ be a positive random variable with support $[c,+\infty[$. We observe $X=X^*+\varepsilon$, where $\varepsilon$ is a symmetric error term. The distribution of $\varepsilon$ is otherwise unknown. Using an iid sample the objective is to estimate $c$. This analysis is in particular motivated by the non-parametric estimation of stochastic cost frontiers. Our method is inspired by recent work. Let us consider the characteristic function of $X$ (denoted by $\psi_X (t)$), which may be easily estimated non-parametrically. The phase of $\psi_X(t)$ (i.e. the ratio of $\psi_X (t)$ by its modulus) does not depend on the distribution of $\varepsilon$, and we use its nonparametric estimator to derive an estimator of $c$.