On nonparametric estimation of intercept and slope distributions in random coefficient regression

• 成果类型: Article
• 署名作者: Beran, R; Feuerverger, A; Hall, P
• 署名单位: University of Toronto; Australian National University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 2569-2592
• 关键词: optimal rates; CONVERGENCE; tomography

摘要

An experiment records stimulus and response for a random sample of cases. The relationship between response and stimulus is thought to be linear, the values of the slope and intercept varying by case. From such data, we construct a consistent, asymptotically normal, nonparametric estimator for the joint density of the slope and intercept. Our methodology incorporates the radial projection-slice theorem for the Radon transform, a technique for locally linear nonparametric regression and a tapered Fourier inversion. Computationally, the new density estimator is more feasible than competing nonparametric estimators, one of which is based on moments and the other on minimum distance considerations.