Nonparametric Testing for Hammerstein Systems

• 成果类型: Article
• 署名作者: Pawlak, Miroslaw; Lv, Jiaqing
• 署名单位: University of Manitoba; AGH University of Krakow
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3171389
• 发表日期: 2022
• 页码: 4568-4584
• 关键词: Central Limit Theorem; dependent data; Hammerstein systems; hermite functions; nonparametric testing; nonparametric identification; U-statistics

摘要

We examine the problem of testing a parametric form of the nonlinearity of Hammerstein systems against a nonparametric alternative. This article proposes test statistics relying on nonparametric orthogonal series regression function estimates. An asymptotic theory of the proposed tests is established including the asymptotic normality under the null hypothesis that the parametric form of the system nonlinearity is correct. Moreover, it is shown that under nonparametric alternatives, the probability of detecting that the parametric model is incorrect tends to one. The rate of detecting local alternatives is also established.