Parametric circular–circular regression and diagnostic analysis
Orathai Polsen, Charles C Taylor · Wiley series in probability and statistics · 2015
We consider various circular–circular regression models in the case of a single explanatory variable and propose a unified framework. We present a useful strategy for estimating parameters of circular–circular regression model that incorporates the approach proposed by Jammalamadaka & SenGupta (2001) with standardization. Our proposed approach for parameter estimation shows a great improvement. In addition, we investigate diagnostic tools for circular regression, in particular an approach for checking the von Mises distribution assumption and a novel method for detecting influential observations. Simulation results suggest that in testing for a von Mises distribution, a score test outperforms Watson's test under certain conditions. Finally, we argue that the sampling distribution of the test statistic for detecting influential observations is a scaled chi-square.