A more powerful test identifying the change in mean of functional data

Buddhananda Banerjee () and Satyaki Mazumder ()
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Buddhananda Banerjee: Indian Institute of Technology Kharagpur
Satyaki Mazumder: Indian Institute of Science Education and Research Kolkata

Annals of the Institute of Statistical Mathematics, 2018, vol. 70, issue 3, No 8, 715 pages

Abstract: Abstract An existence of change point in a sequence of temporally ordered functional data demands more attention in its statistical analysis to make a better use of it. Introducing a dynamic estimator of covariance kernel, we propose a new methodology for testing an existence of change in the mean of temporally ordered functional data. Though a similar estimator is used for the covariance in finite dimension, we introduce it for the independent and weakly dependent functional data in this context for the first time. From this viewpoint, the proposed estimator of covariance kernel is more natural one when the sequence of functional data may possess a change point. We prove that the proposed test statistics are asymptotically pivotal under the null hypothesis and consistent under the alternative. It is shown that our testing procedures outperform the existing ones in terms of power and provide satisfactory results when applied to real data.

Keywords: Change point detection; Functional data analysis; Covariance kernel (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10463-017-0606-0

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