Some of Parametric and Non Parametric Estimations for Circular Regression Model via Simulation

Abstract

Circular data, or circular observations, is data that has a periodic nature and is measured on the unit circle in radians or degrees. It differs fundamentally from linear data that is compatible with the mathematical representation of the usual linear regression model due to its periodic nature. Circular data arises in a wide variety of fields of life, including scientific, medical, economic, and social. Circular (angular) regression is one of the most important statistical methods that represent this data. There are several methods for estimating angular regression, including parametric and non-parametric methods. The problem of the research appears in dealing with circular data when using angular measurement for the study variables in the regression model, whether the dependent variable y or the explanatory variables x,s, or both together, due to the presence of the periodic property in the circular scale.

The research aims to estimate the models that represent these phenomena subject to the logic of circular angular data, taken under the presence of the periodic property over 24 hours in the measurement. The research also aims to apply causal modeling using a regression model based on a trigonometric transformation function, which will result in a change in the structure of the natural equations that lead to finding solutions to them to estimate the regression coefficients.

Therefore, the research included the use of three models for angular regression, two of which are parametric models and one is a non-parametric model. As for the parametric models, they are the Maximum Likelihood Circular (MLE) model and the Circular Shrinkage Regression (DM) model. This method is a method proposed by the researcher. As for the non-parametric model, it is the Local Linear Circular Regression (LL) model. The Mean Circular Error (MCE) criterion was used to compare the three models.

The results in the experimental (simulation) side showed that the parametric models are not better than the non-parametric model in solving the problem of non-Euclidean data that deals with circular observations using the inverse transformation method in simulation experiments (9 experiments) and for all assumed values and all sample sizes.