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

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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 

Notes

Acknowledgements

The authors are thankful to the British Atmospheric Data Centre and Carbon Dioxide Information Analysis Center for real data. The Daily Central England Temperature data have been taken from the Hadley Centre for Climate Prediction and Research (2007), and monthly global average anomaly of temperatures is taken from Jones et al. (2013). The authors also thank the anonymous referee for his insightful comments and suggestions which helped to make a significant improvement of the manuscript.

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Department of Mathematics and StatisticsIndian Institute of Science Education and Research KolkataMohanpurIndia

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