@article{e98cb387c9934c6c8782db63c944ba67,
title = "On circular correlation for data on the torus",
abstract = "The circular correlation topic for data on the torus is studied. Firstly, the order for two points on the circumference is considered and an order function is defined. Then, an alternative moment coefficient to measure T-linear association between two circular variables based on the order function is proposed. After the concordant on the torus is explained, an alternative rank correlation coefficient on the torus is also proposed. A number of properties for the two coefficients are investigated and their comparisons with the existing alternatives are made. Two examples of real data analysis are presented to illustrate our results.",
keywords = "Circular correlation, Circular data, Circular order, Kendall{\textquoteright}s $$\tau $$τ, T-linear, Kendall{\textquoteright}s τ, Kendall's tau",
author = "Xiaoping Zhan and Tiefeng Ma and Shuangzhe Liu and Kunio Shimizu",
note = "Funding Information: We would like to thank very much the Editor and reviewers for their constructive and useful comments which led to an improved presentation of the manuscript. The work of the first two authors is supported by the National Natural Science Foundation of China (No. 11471264, 11401148, 11571282). Publisher Copyright: {\textcopyright} 2017, Springer-Verlag Berlin Heidelberg. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2019",
month = dec,
doi = "10.1007/s00362-017-0897-5",
language = "English",
volume = "60",
pages = "1827--1847",
journal = "Statistical Papers",
issn = "0932-5026",
publisher = "Springer",
number = "6",
}