Estimation of the Boundary of a Variable Observed With Symmetric Error. Issue 529 (2nd January 2020)

• Record Type: Journal Article
• Authors: Florens, Jean-Pierre; Simar, Léopold; Van Keilegom, Ingrid
• Is Part Of: Journal of the American Statistical Association. Volume 115:Issue 529(2020)
• Page Start: 425
• Page End: 441
• Publication Date: 2020-01-02
• Subjects: Characteristic function -- Cumulant function -- Flexible parametric family -- Frontier estimation -- Laguerre polynomials; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2018.1555093
• Languages: English
• ISSNs: 0162-1459

Abstract

Abstract: Consider the model Y = X + ε with X = τ + Z, where τ is an unknown constant (the boundary of X ), Z is a random variable defined on R +, 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 Y = τ ( w 1, w 2 ) + Z + ε, 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.