4.2 Article

Ratio detection for mean change in α mixing observations

Journal

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 48, Issue 7, Pages 1693-1708

Publisher

TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2018.1438623

Keywords

Consistence; change point; estimator; median; ratio test

Funding

  1. National Natural Science Foundation of China [11226217, 71501115]
  2. Natural Science Foundation for Youths of Shanxi Province [201701D221003]
  3. Shanxi Scholarship Council of China [2016-015]
  4. Postdoctoral Science Foundation
  5. Postdoctoral Science Special Foundation of China [2012M510772, 2013T60266]
  6. Humanity and Social Science Foundation of Ministry of Education of China [14YJA790034]
  7. National Social Science Foundation of China [15BJY164]

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A ratio test based on the indicators of the data minus the sample median is proposed to detect the change in the mean of alpha-mixing stochastic sequences. The asymptotic distribution of the test is derived under the null hypothesis. The consistency of the proposed test is also obtained under the hypothesis that mu changes at some unknown time. We also propose a consistent estimator for the change point on the ratio test. Simulations demonstrate that the test and the estimator behaves well for heavy-tailed sequences. At last, an empirical application demonstrate the validity of the test and the estimator.

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