On the choice of the two tuning parameters for nonparametric estimation of an elliptical distribution generator
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916624716529664 |
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| author | Ryan, Victor Derumigny, Alexis |
| author_facet | Ryan, Victor Derumigny, Alexis |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the choice of the two tuning parameters for nonparametric estimation of an elliptical distribution generator Ryan, Victor Derumigny, Alexis Statistics Theory Methodology 62H12, 62G05 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. |
| title | On the choice of the two tuning parameters for nonparametric estimation of an elliptical distribution generator |
| topic | Statistics Theory Methodology 62H12, 62G05 |
| url | https://arxiv.org/abs/2408.17087 |