One-step R-estimation in linear models with stable errors |
| |
Authors: | Marc Hallin Yvik Swan Thomas Verdebout David Veredas |
| |
Affiliation: | 1. ECARES, Université libre de Bruxelles, Belgium;2. ORFE, Princeton University, United States;3. Académie Royale de Belgique; CentER, Tilburg University, Netherlands;4. Unité de Recherche en Mathématiques, Université du Luxembourg, Luxembourg;5. Département de Mathématique, Université libre de Bruxelles, Belgium;6. EQUIPPE-GREMARS, Université Lille Nord de France, France;g Solvay Business School of Economics and Management, Université libre de Bruxelles, Belgium |
| |
Abstract: | Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step R-estimation method and investigate its asymptotic performances under stable densities. Contrary to traditional least squares, the proposed R-estimators remain root-n consistent (the optimal rate) under the whole family of stable distributions, irrespective of their asymmetry and tail index. While parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (α0,b0) of the tail index α and skewness parameter b, while preserving root-n consistency under any (α,b) as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances. |
| |
Keywords: | Stable distributions Local asymptotic normality LAD estimation R-estimation Asymptotic relative efficiency |
本文献已被 ScienceDirect 等数据库收录! |
|