Estimation of a semiparametric transformation model

• 成果类型: Article
• 署名作者: Linton, Oliver; Sperlich, Stefan; Van Keilegom, Ingrid
• 署名单位: University of London; London School Economics & Political Science; University of Gottingen; Universite Catholique Louvain
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000848
• 发表日期: 2008
• 页码: 686-718
• 关键词: nonparametric-estimation; REGRESSION-MODEL; likelihood; CONVERGENCE; integration; rates

摘要

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parameter maximizing a profile likelihood function or minimizing the mean squared distance from independence. First the problem of identification of such models is discussed. We then state asymptotic results for a general class of nonparametric estimators. Finally, we give some particular examples of nonparametric estimators of transformed separable models. The small sample performance is studied in several simulations.