Procedure for Detecting Outliers in a Circular Regression Model

Abstract

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia’s model are studied via simulations. For illustration, we apply the procedure on circadian data.

Review on Outliers Identification Methods for Univariate Circular Biological Data

“…Other studies have been done on eye and circadian rhythm data set but for Multiple Circular Regression (MCR) model. [10] using DMCEs Statistic to analyse circadian data base on systolic blood pressure. The DMCEs Statistic performed well when the sample size n and the value of concentration parameter κ are large.…”

“…Thus, a lot of study has been done to identify outliers in biological data, but most of them for circular regression model. For example on eye dataset of glaucoma patient [8,9], on circadian data taken from systolic blood pressure reading [10] and on angular of protein chain shapes [11]. Hence, there is a need to explore more outliers' detection technique for univariate circular biological data.…”

An Outlier Detection Method for Circular Linear Functional Relationship Model Using Covratio Statistics

“…The covratio statistics have long been used to identify outlier in linear regression models via a row deletion approach. Some studies on detecting outliers have been discussed by Abuzaid et al (2011), , Ghapor et al (2014) and Rambli et al (2016). The covratio statistic is used to measure the effect of removing the observation based on the determinantal ratio given by:…”

A New Discordancy Test on a Regression for Cylindrical Data

“…Abuzaid et al (2011) and Ibrahim et al (2013) extended the COVRATIO statistic that is used in linear regression to a circularcircular regression model. Abuzaid et al (2013) and Rambli et al (2016) proposed new outlier detection methods in the circular-circular regression models called mean circular error statistic by using row-deletion method. Rambli et al (2016) transformed the residuals into linear scales using a trigonometric function while Abuzaid et al (2013) used the circular distance between two circular observations.…”

“…Abuzaid et al (2013) and Rambli et al (2016) proposed new outlier detection methods in the circular-circular regression models called mean circular error statistic by using row-deletion method. Rambli et al (2016) transformed the residuals into linear scales using a trigonometric function while Abuzaid et al (2013) used the circular distance between two circular observations. While different outlier detection procedures have been developed for linear and circular regression models, no such work has been done on the regression model for cylindrical data.…”