A0504
Title: Data-based bin width selection for rose diagram
Authors: Yasuhito Tsuruta - The University of Nagano (Japan) [presenting]
Abstract: A rose diagram is a representation that circularly organizes data with the bin width as the central angle. This diagram is widely used to display and summarize circular data. Some studies have proposed the selector of bin width based on data. However, only a few papers have discussed the property of these selectors from a statistical perspective. Thus, the aim is to provide a data-based bin width selector for rose diagrams using a statistical approach such as minimizing an error criterion. The radius of the rose diagram is considered to be a nonparametric estimator of the square root of two times the circular density. The mean integrated square error of the rose diagram and its optimal bin width is derived, and two new selectors are proposed: normal reference rule and biased cross-validation. The normal reference rule is a parametric method assuming an underlying density is a von Mises density. Biased cross-validation is a nonparametric method without the specification of an underlying density. It is shown that biased cross-validation converges to its optimizer. The numerical experiment is conducted under some simulation scenarios based on sine-skewed distributions to investigate how a choice of bin width affects the performance of the rose diagram under finite samples. Its result shows that biased cross-validation or normal reference rule outperforms some previous selectors and biased cross-validation has the best performance.
