{"title":"On the choice of the two tuning parameters for nonparametric estimation of an elliptical distribution generator","authors":"Victor Ryan, Alexis Derumigny","doi":"arxiv-2408.17087","DOIUrl":null,"url":null,"abstract":"Elliptical distributions are a simple and flexible class of distributions\nthat depend on a one-dimensional function, called the density generator. In\nthis article, we study the non-parametric estimator of this generator that was\nintroduced by Liebscher (2005). This estimator depends on two tuning\nparameters: a bandwidth $h$ -- as usual in kernel smoothing -- and an\nadditional parameter $a$ that control the behavior near the center of the\ndistribution. We give an explicit expression for the asymptotic MSE at a point\n$x$, and derive explicit expressions for the optimal tuning parameters $h$ and\n$a$. Estimation of the derivatives of the generator is also discussed. A\nsimulation study shows the performance of the new methods.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"144 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - STAT - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.17087","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.