Abstract Consider the model with , where τ is an unknown constant (the boundary of X), Z is a random variable defined on , ε is a symmetric error, and ε and Z are independent. Based on an iid sample of Y, we aim at identifying and estimating the boundary τ when the law of ε is unknown (apart from symmetry) and in particular its variance is unknown. 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. The paper also proposes an extension to stochastic frontier analysis, where the model is conditional to observed variables. The model becomes , where Y is a cost, w1 are the observed outputs and w2 represents the observed values of other conditioning variables, so Z is the cost inefficiency. Some simulations illustrate again how the approach works in finite samples, and the proposed procedure is illustrated with data coming from post offices in France.

中文翻译：

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估计具有对称误差的变量的边界

摘要 考虑具有 的模型，其中 τ 是未知常数（X 的边界），Z 是定义在 上的随机变量，ε 是对称误差，ε 和 Z 是独立的。基于 Y 的 iid 样本，我们的目标是在 ε 定律未知（对称性除外），特别是其方差未知时识别和估计边界 τ。我们提出了一种基于最小距离方法并利用拉盖尔多项式的估计程序。显示了渐近结果以及有限样本模拟。该论文还提出了对随机前沿分析的扩展，其中模型以观察到的变量为条件。模型变为 ，其中 Y 是成本，w1 是观察到的输出，w2 表示其他条件变量的观察值，所以 Z 是成本低效。