Subsampling tests for the mean change point with heavy-tailed innovations

Authors:
Hao Jin;Zheng Tian;Ruibing Qin
Affiliations:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China and State Key Laboratory of Remote Sensing Science, Chinese Academy of Sciences, Beijing 1001 ...;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

The quest of the mean change point with innovations in the domain of attraction of a κ-stable law appears to still be ongoing. We adopt the residual CUSUM of squares test (RCUSQ) and derive its null asymptotic distribution, which is dependent on stable index κ. Then a residual-based subsampling is proposed to approximate the null distribution when stable index κ is unknown. Consistency and the rate of convergence for the estimated change point are also obtained. We establish the asymptotic validity of this method and assess its performance both theoretically and numerically.