Circular Functional Relationship Model with Wrapped Cauchy Errors

Ali Hassan Abuzaid, Walaa Abu El-laban, Abdul Ghapor Hussin

Abstract


This paper extends the simple linear regression model with wrapped Cauchy error to the functional case when both variables are subjected to wrapped Cauchy errors. Assuming the ratio between the two error variances is known and the slope parameter equals one the maximum likelihood estimates are obtained. The closed-form expression for the maximum likelihood estimators are not available and the estimates are obtained iteratively by choosing a suitable initial values. The quality of estimates and the accuracy of the model are illustrated via simulations and the results revealed an acceptable performance of the estimators where they are unbiased, consistent and robust. The sampling variances of the model parameters are obtained via bootstrapping methods and consequently the confidence intervals were constructed. The proposed model is illustrated with an application on the analysis of wind directions data at two cities in the Gaza strip, Palestine.


Keywords


Bootstrap; EIVM; robustness; wind direction

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DOI: http://dx.doi.org/10.18187/pjsor.v14i2.1858

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Title

Circular Functional Relationship Model with Wrapped Cauchy Errors

Keywords

Bootstrap; EIVM; robustness; wind direction

Description

This paper extends the simple linear regression model with wrapped Cauchy error to the functional case when both variables are subjected to wrapped Cauchy errors. Assuming the ratio between the two error variances is known and the slope parameter equals one the maximum likelihood estimates are obtained. The closed-form expression for the maximum likelihood estimators are not available and the estimates are obtained iteratively by choosing a suitable initial values. The quality of estimates and the accuracy of the model are illustrated via simulations and the results revealed an acceptable performance of the estimators where they are unbiased, consistent and robust. The sampling variances of the model parameters are obtained via bootstrapping methods and consequently the confidence intervals were constructed. The proposed model is illustrated with an application on the analysis of wind directions data at two cities in the Gaza strip, Palestine.


Date

2018-06-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 14 No. 2, 2018



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810