Outlier detection methods of unreplicated linear functional relationship model for circular variables

This study is on modelling circular data and proposed several methods of detecting outliers of the model considered in the study. In particular, the linear functional relationship model is considered where the maximum likelihood parameters and the covariance matrix are derived for the case where the error concentration parameters are unequal since previous study only considered the parameter estimation for the case of equal error concentration. The parameter estimate of x variable is improved by applying the iterative procedure in which the incidental parameter stops accumulating after the values converge to a finite number. The parameter estimate of the concentration parameter is estimated by using modified Bessel function in which it is expanded to become a cubic function. Monte Carlo simulation study shows that the proposed parameter estimations give a small bias with mean resultant length near to 1 and small estimated root meansquare errors that indicate an adequacy of the estimation. Next, some methods to detect the presence of outlier in circular data are discussed. Previous studies only considered outlier detection methods for equal error concentration case. Therefore, in this thesis, all outlier detection methods take into account of both equal and unequal error concentration parameters in the model. The first proposed method in outlier detection is by using the determinantal equation of the covariance matrix, called covratio, in which the covariance matrix is based on the one derived in the first part of the study. Another two proposed methods used to detect the outlier are by using the difference mean circular errors. The two trigonometric functions are the cosine (FDMCEC) and sine (FDMCES) functions. The cut-off equations are derived based on the 5% upper percentile of the simulation study for each method for 95% confident level. The feasibility of all of the methods is assessed by the power of performance in Monte Carlo simulation studies when outlier is planted in the data. The results from the simulation study suggest that the power of performance for all three outlier detection methods achieves the maximum percentage which is 100% as the level of contamination increases. Hence, this suggests the feasibility of the method used in outlier detection.