New COVRATIO Statistic for Outlier Detection in Simultaneous Linear Functional Relationship Model and Its Application in Malacca Environmental Dataset

Abstract

Environmental studies, such as monsoon analysis, require examining relationships between multiple linear variables like wind speed, humidity, and temperature, with consideration of errors in each variable. Outliers in the data may affect the accuracy of analysis. This study aims to develop and validate a novel method for detecting outliers in simultaneous linear functional relationship model (LFRM) using the COVRATIO statistic. The objectives include deriving cut-off points for outlier detection using Monte Carlo simulations and demonstrating the method’s effectiveness on synthetic and real-world environmental datasets from Malacca. The findings confirm that the proposed method accurately identifies outliers, with detection performance improving as the variance of data contamination increases. Application to Malacca’s environmental data during the 2020 southwest monsoon season revealed significant outliers in the relationship between wind speed and humidity, while no outliers were found for wind speed and temperature. Removing detected outliers resulted in improved parameter estimates and reduced variance, enhancing the reliability of the LFRM. Data normality was verified through Q-Q plots and the Kolmogorov-Smirnov test statistic, demonstrating the robustness and applicability of the method in environmental studies.