Semi-parametric estimation tn the nonlinear structural errors-in-variables model

• 成果类型: Article
• 署名作者: Taupin, ML
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/996986502
• 发表日期: 2001
• 页码: 66-93
• 关键词: LIKELIHOOD-ESTIMATION; Optimal Rates; CONVERGENCE; regression; density

摘要

In the nonlinear structural errors-in-variables model, we propose a consistent estimator of the unknown parameter using a modified least squares criterion. We give an upper bound of its rate of convergence which is strongly related to the regularity of the regression function and is generally slower than the parametric rate of convergence n(-1/2). Nevertheless, the rate is of order n-(1/2) for some particular analytic regression functions. For instance, when the regression Function is either a polynomial function or an exponential function, we prove that our estimator achieves the parametric rate of convergence.