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On the choice of the two tuning parameters for nonparametric estimation of an elliptical distribution generator
Victor Ryan, Alexis Derumigny
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Elliptical distributions are a simple and flexible class of distributions that depend on a one-dimensional function, called the density generator. In this article, we study the non-parametric estimator of this generator that was introduced by Liebscher (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. Estimation of the derivatives of the generator is also discussed. A simulation study shows the performance of the new methods.
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