Efficient nonparametric inference for discretely observed compound Poisson processes

• 成果类型: Article
• 署名作者: Coca, Alberto J.
• 署名单位: University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0761-5
• 发表日期: 2018
• 页码: 475-523
• 关键词: exponential levy models; empirical characteristic function; DENSITY-ESTIMATION; LIMIT-THEOREMS; low-frequency; random sums; calibration; estimators; deconvolution

摘要

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L,vy distributions are proposed and functional central limit theorems using the uniform norm are proved for both under mild conditions. The limiting Gaussian processes are identified and efficiency of the estimators is established. Kernel estimators for the mass function, the intensity and the drift are also proposed, their asymptotic properties including efficiency are analysed, and joint asymptotic normality is shown. Inference tools such as confidence regions and tests are briefly discussed.