Estimation of the Boundary of a Variable Observed With Symmetric Error

• 成果类型: Article
• 署名作者: Florens, Jean-Pierre; Simar, Leopold; Van Keilegom, Ingrid
• 署名单位: Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite Catholique Louvain; KU Leuven
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1555093
• 发表日期: 2020
• 页码: 425-441
• 关键词: frontier estimation; models; density; point

摘要

Consider the model with , where tau is an unknown constant (the boundary of X), Z is a random variable defined on , 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. 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, w(1) are the observed outputs and w(2) 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.