Parameter Estimation of the JS Robust Circular Regression Model for Corneal Convolution Data

Abstract

In this research, we used real data about the eye obtained from the Jannah Laboratory for advanced diagnostic examinations of eye diseases using a retinal incision OCT device for three-dimensional computed tomography, in which pictures were taken of the back part of the eyes of (100) patients using computed tomography of the front part of the visual range. The two variables that represent the studied data are the independent variable (U), which represents the angle in radians, which measures the posterior curvature of the cornea, and the second variable is the dependent variable (V), which represents the angle of the eye between the posterior curvature of the cornea and the iris. The data was tested to contain outliers using the COVARATIO statistic, and it was found that the data contained outliers. Five estimation methods were applied, the JS circular regression model, namely the circular least squares method, the M estimator method, the circular truncated least squares estimator, the MM estimator method, and the S estimator method. The superiority of the M estimator method over other estimation methods in estimating the parameters of the JS circular regression model was reached.