On the Choice of the Two Tuning Parameters for Nonparametric Estimation of an Elliptical Distribution Generator
Victor Ryan (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Alexis Derumigny (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
Elliptical distributions are a simple and flexible class of distributions that depend on a one-dimensional function, called the density generator. In this chapter, we study the nonparametric estimator of this generator that was introduced by Liebscher (J Multivariate Anal 92(1):205–225, 2005). This estimator depends on two tuning parameters: a bandwidth h—as usual in kernel smoothing—and an additional parameter a that control the behavior near the center of the distribution. We give an explicit expression for the asymptotic MSE at a point x and derive explicit expressions for the optimal tuning parameters h and a. The estimation of the derivatives of the generator is also discussed. A simulation study shows the performance of the new methods.