Alternative Methods for Detecting Outliers in Circular Data

Abstract

The research contains of English and Arabic summary, a list of abbreviations and a list of references. It also outlines in five chapters as follows In most model selection problems the number of parameters should be large and grow with the sample size. Circular data as any other types of data are subjected to contaminate with some unexpected observations. Outliers in the context of circular data would be defined as a set of observations which is inconsistent with the rest of the sample. It is expected to lay far from the mean direction of the circular sample. We studied two methods to detect outliers in circular data such as kernel density function (KDF) and penalized maximum likelihood (PML). The first method discussed an outlier in circular data using kernel density function (KDF) with experiments of two datasets and identify the points as a cluster points and this being an outlier. Local Outlier Factor (LOF), which is based on the density estimate theory play a basic algorithm, however, LOF has two disadvantages that restrict its performance in outlier detection. Besides, we propose an algorithm which is more suitable for outlier detection in circular data by the local density factor (LDF). We discuss this algorithm for outlier detection which find the outliers by comparing the local density of each point to the local density of its neighbors in circular data. On the other hand, the second method detect an outliers in logistic circular data with algorithms and R program. In this method, we have a rainfall data as an application for this model. In penalized maximum likelihood (PML), we develop some methods from linear model and convert these method in circular data as penalized least squares (PLS), smoothly clipped absolute deviation (SCAD) and new unified algorithm (NUA). We use local linear approximation (LLA) algorithm to approximate the parameters in logistic regression model for circular data which is intended to describe the relationship between a binary response and circular predictor(s).