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 Zp, 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.

Estimation of parameters in multivariate wrapped models for data on a p-torus / Nodehi, Anahita; Golalizadeh, Mousa; Maadooliat, Mehdi; Agostinelli, Claudio. - In: COMPUTATIONAL STATISTICS. - ISSN 0943-4062. - 2021, 36:1(2021), pp. 193-215. [10.1007/s00180-020-01006-x]

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

Agostinelli, Claudio
2021-01-01

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 Zp, 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.
2021
1
Nodehi, Anahita; Golalizadeh, Mousa; Maadooliat, Mehdi; Agostinelli, Claudio
Estimation of parameters in multivariate wrapped models for data on a p-torus / Nodehi, Anahita; Golalizadeh, Mousa; Maadooliat, Mehdi; Agostinelli, Claudio. - In: COMPUTATIONAL STATISTICS. - ISSN 0943-4062. - 2021, 36:1(2021), pp. 193-215. [10.1007/s00180-020-01006-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/286866
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