Robust detection of outliers in both response and explanatory variables of the simple circular regression model

• Main Authors: Rana, Sohel, Mahmood, Ehab A., Midi, Habshah, Hussin, Abdul Ghapor
• Format: Article
• Language: English
• Published: Institute for Mathematical Research, Universiti Putra Malaysia 2016
• Online Access: http://psasir.upm.edu.my/id/eprint/52338/1/12.%20Sohel.pdf; http://psasir.upm.edu.my/id/eprint/52338/; http://einspem.upm.edu.my/journal/fullpaper/vol10no3/12.%20Sohel.pdf

It is very important to make sure that a statistical data is free from outliers before making any kind of statistical analysis. This is due to the fact that outliers have an unduly affect on the parameter estimates. Circular data which can be used in many scientific fields are not guaranteed to be free from outliers. Often, the relationship between two circular variables is represented by the simple circular regression model. In this respect, outliers might occur in the both response and explanatory variables of the circular model. In circular literature, some researchers show interest to identify outliers only in the response variable. However, to the best of our knowledge, no one has proposed a method which can detect outliers in both the response and explanatory variables of the circular linear model. Thus, in this article, an attempt has been made to propose a new method which can detect outliers in both variables of the simple circular linear model. The proposed method depends on the robust circular distance between the response and the explanatory variables in the model. Results from the simulations and real data example show the merit of our proposed method in detecting outliers in simple circular model.