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

Abstract

The existence of outlier may affect data aberrantly. However, outlier detection problem has been frequently discussed for linear data but limited on circular data. Thus, this paper discusses an outlier detection method on circular data. We focus on circular data with equal error concentration parameters where the data is studied using linear functional relationship model. In this paper, the data and the error terms are distributed with von Mises distribution. We modify the covratio statistics in which the correction factor is applied to the estimation of concentration parameter. We develop the cut-off equation based on the 5% upper percentile of the covratio statistics and the power of performance of outlier detection is examined by a Monte Carlo simulation study. The simulation result shows that the power of performance increases when the concentration and the level of contamination increase. The applicability of the proposed method is illustrated by using the wind direction data collected from the Holderness Coastline at the Humberside Coast in North Sea, United Kingdom.

Detection of Outliers in Circular Regression Model Via DFBETAcIS Statistic

“…When the DFBETAc IS statistic is applied to wind direction data, observations 38 and 111 are identified as outliers, which similar observations detected as found in Abuzaid (2010), Mokhtar et al (2019) and Rambli et al (2015). The exclusion of these two observations from the original data set improves the fitted JSCRM.…”

“…However, it is also supported that the COVRATIO statistic in Rambli et al (2015) and Mokhtar et al (2019), D, M, A, and Chord Statistics (Abuzaid 2010) show the same results when applied to wind direction data. Therefore, the exclusion of these two observations from the original data set improves the goodness-of-fit for the model.…”

Modelling Wind Speed, Humidity, and Temperature in Butterworth and Melaka during Southwest Monsoon in 2020 with a Simultaneous Linear Functional Relationship

“…The existing research uses the bivariate LFRM to study the relationship between two linear variables (Arif et al, 2020b;Ghapor et al, 2014). Therefore, this study extends the work of Ghapor et al (2014) by extending the bivariate LFRM to simultaneous LFRM, allowing for the statistical examination of relationships among more than two linear variables, while considering measurement errors.…”

“…Because it considers the presence of error across all parameters, EIVM is the most statistically relevant tool for predicting reactivity ratios. EIVM is classified into three types: functional, structural, and ultrastructural (Ghapor et al, 2014;Jamaliyatul et al, 2023). A functional relationship model between X and Y is when X is a mathematical variable or fixed constant.…”

“…To the best of the author's knowledge, the bivariate LFRM model has been extended to the simultaneous LFRM to study the relationship between multiple circular variables, representing a novel contribution to existing literature (Mokhtar et al, 2015). The existing research uses the bivariate LFRM to study the relationship between two linear variables (Arif et al, 2020b;Ghapor et al, 2014). Therefore, this study extends the work of Ghapor et al (2014) by extending the bivariate LFRM to simultaneous LFRM, allowing for the statistical examination of relationships among more than two linear variables, while considering measurement errors.…”