Estimation of parameters in multivariate wrapped models for data on a p-torus

Abstract

Multivariate circular observations, i.e. points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, the statistical inference based on such models is quite complicated since each contribution in the log-likelihood function involves an infinite sum of indices in \({\mathbb {Z}}^p\), where p is the dimension of the data. To overcome this problem, for moderate dimension p, we propose two estimation procedures based on Expectation-Maximisation and Classification Expectation-Maximisation algorithms. We study the performance of the proposed techniques on a Monte Carlo simulation and further illustrate the advantages of the new procedures on three real-world data sets.

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Acknowledgements

This research is supported in part by a grant BS-1395-01-07 from the Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.

The authors thank Stephan Huckemann and Benjamin Eltzner for providing the RNA data set. We would also like to thank the editor, and two referees for their constructive and thoughtful comments which helped us tremendously in improving the manuscript.

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Correspondence to Mousa Golalizadeh.

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Nodehi, A., Golalizadeh, M., Maadooliat, M. et al. Estimation of parameters in multivariate wrapped models for data on a p-torus. Comput Stat 36, 193–215 (2021). https://doi.org/10.1007/s00180-020-01006-x

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Keywords

  • CEM algorithm
  • EM algorithm
  • Estimation procedures
  • Multivariate wrapped distributions
  • Torus