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Title: Improve direct plug-in rule selector for circular kernel density estimation Authors:  Yasuhito Tsuruta - The University of Nagano (Japan) [presenting]
Abstract: A circular kernel density estimation is a nonparametric method for exploring the density structure of circular data without model specifications because it flexibly changes its shape through the choice of the smoothing parameter. A huge smoothing parameter leads to undersmoothing, and the density plot looks like a multimodal density and brings wasteful zigzags. Whereas a small smoothing parameter leads to oversmoothing, and the density plot looks like a unimodal distribution and hides all non-unimodal distribution properties. It requires appropriately selecting a smoothing parameter. The optimal parameter as the minimizer of the mean integrated error depends on a functional of an underlying density. Therefore, there is a lot of research on estimating the optimal smoothing parameter. The direct plug-in rule (DPI) selector is the kernel functional estimator for the optimal parameter. However, DPI selector also requires choosing the pilot smoothing parameter. The minimizer of the mean squared error of its selector also depends on the functional of an underlying density. Therefore, a new kernel functional estimator for its pilot parameter is proposed. The proposed estimator is shown to be asymptotic normal and consistent. The numerical experiment is conducted to investigate the small sample characteristic of the proposed estimator.