A method for detecting outliers in linear-circular non-parametric regression

Area of Science:

• Statistics
• Data Science

Background:

• Non-parametric regression is crucial for modeling complex relationships.
• Outliers in the response variable can significantly distort regression results.
• Linear-circular regression is used for data with both linear and circular components.

Purpose of the Study:

• To propose a robust outlier detection method for non-parametric linear-circular regression.
• To address challenges posed by outliers in the response variable when residuals follow a Wrapped-Cauchy distribution.
• To evaluate the performance of the proposed method under various conditions.

Main Methods:

• Development of a robust outlier detection method utilizing the circular median.
• Application of Nadaraya-Watson and local linear regression for non-parametric fits.
• Performance evaluation through a real dataset analysis and comprehensive simulation studies.

Main Results:

• The proposed method demonstrates robust performance, particularly at medium to high contamination levels.
• Method efficacy improves with increased sample size and data homogeneity.
• Local linear estimation outperforms Nadaraya-Watson when outliers are present in the response variable.

Conclusions:

• The circular median-based outlier detection method offers a reliable solution for non-parametric linear-circular regression with contaminated data.
• The choice of regression fitting method (Local Linear Estimation vs. Nadaraya-Watson) impacts performance in the presence of outliers.
• The study highlights the importance of sample size and data homogeneity for robust statistical modeling.