Detection of outliers in the complex linear regression model

The existence of outliers in any type of data affects the estimation of models’ parameters. To date there are very few literatures on outlier detection tests in circular regression and it motivated us to propose simple techniques to detect any outliers. This paper considered the complex linear regression model to fit circular data. The complex residuals of complex linear regression model were expressed in two different ways in order to detect possible outliers. Numerical example of the wind direction data was used to illustrate the efficiency of proposed procedures. The results were very much in agreement with the results obtained by using the circular residuals of the simple regression model for circular variables

Detection of outliers in simple circular regression models using the mean circular error statistic

The investigation on the identification of outliers in linear regression models can be extended to those for circular regression case. In this paper, we propose a new numerical statistic called mean circular error to identify possible outliers in circular regression models by using a row deletion approach. Through intensive simulation studies, the cut-off points of the statistic are obtained and its power of performance investigated.It is found that the performance improves as the concentration parameter of circular residuals becomes larger or the sample size becomes smaller. As an illustration, the statistic is applied to a wind direction data set