Robust detection measures and robust parameter estimation methods in circular univariate and simple circular regression model

The univariate and the simple circular regression model can be used in many scientific fields. There is evidence that the classical methods to estimate the parameters are adversely affected by outliers. Hence, it is very crucial to detect outliers in circular data. Some existing methods such as Mardia, M, A, and Chord are developed in this regard. Unfortunately, these methods are formulated to identify only a single outlier. Hence, we propose robust circular distance (RCDu) statistic to identify a single and multiple outliers in the univariate circular data. The results of the study indicate that the RCDu statistic is successful in detecting outliers with smaller masking and swamping rates. Not much research is focused on the robust estimation of univariate circular distribution when the circular data have outliers. Thus, robust methods are proposed to estimate the circular location parameter, circular variance and mean resultant length of von Mises distribution. The findings signify that the two proposed methods have done a credible job compared to other methods in this study. This thesis also addresses the issue of existing outliers in the simple circular regression model. Not much consideration is given to investigate the identification methods of outliers in such model. Hence, we propose robust circular distance (RCDy) statistic to detect outliers in the response variable of the simple circular regression model. The results of the study indicate that the RCDy has the highest proportion of detection outliers with the lowest rate of masking. To the best for our knowledge, no research is focused on the detection of outliers in the response and the explanatory variables of a simple circular regression model. Hence, robust circular distance (RCDxy) statistic is formulated to detect outliers in the response and the explanatory variables. The results show that the RCDxy statistic is very successful to detect outliers with low rates of masking and swamping. The maximum likelihood estimator (MLE) is the commonly used method to estimate model parameters of the simple circular regression model. However, the MLE is inefficient if the circular data have outliers. To the best of our knowledge, no work has been done to propose robust method to estimate parameters of the simple circular regression model when the response variable has outliers. Therefore, the robust MWLE 1 and MWLE 2 are developed. The findings indicate that the MWLE2 and the MWLE1 are more efficient than the MLE. To date, there is no robust parameters estimation method of a simple circular regression model is developed when outliers are present in the response and the explanatory variables. Therefore, two robust estimators namelyMWLE1 and MWLE2 are established. The results show that the performance of the MWLE2 and the MWLE1 are more efficient than the MLE when outliers are present in both X and Y directions.

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