Some statistical problems on circular simultaneous functional relationship model

This study focuses on parameter estimation and outlier detection within the circular simultaneous functional relationship model (CSFRM), considering both equal and unequal variances. The model for unequal variance is a newly proposed extension from the previous model of equal variances. Two approaches, the minimum sum (ms) and polyroot functions, are employed to approximate parameter estimates due to the complexity of the log-likelihood function. Simulation studies demonstrate reduced bias in the parameter estimates, indicating their effectiveness. Confidence intervals for model parameters are constructed using covariance matrices. Simulation results demonstrate the superiority of the Bootstrap Confidence Interval (BCI) method in constructing confidence intervals for estimated parameters. Additionally, a novel modification method is proposed for identifying single outliers in CSFRM for cases of unequal variances, utilizing the Simultaneous Functional Difference Mean Circular Error cosine (SFDMCEc). Simulation results show SFDMCEc's robustness in outlier detection as contamination levels increase. Overall, this study presents effective techniques for parameter estimation, confidence interval and outlier detection in CSFRM, with promising performance in simulation studies for practical applications involving circular simultaneous functional relationships.