Asymptotic and Qualitative Performance of Non-Parametric Density Estimators: A Comparative Study
Asymptotic and Qualitative Performance of Non-Parametric Density Estimators: A Comparative Study
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DOI：
10.1111/j.1368-423x.2008.00249.x
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发表时间：
2008-04
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影响因子：
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通讯作者：
Teruko Takada
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文献类型：
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作者：
Teruko Takada
受金融应用的启发，我们评估了几种单变量密度估计方法的性能，重点考察了它们处理重尾目标密度的能力。比较了固定带宽核估计器、自适应带宽核估计器、Gallant和Nychka的Hermite级数(SNP)估计器以及Koperberg和Stone的对数样条估计器四种估计方法。我们的结论是，对数样条法和自适应核方法具有更好的性能，而且SNP估计器的收敛速度明显慢于其他方法。SNP估计量的Hellinger收敛速度是尾部重量的函数。这些发现在蒙特卡罗实验中得到了证实。定性评估揭示了固定核和SNP估计的尾部的旁瓣可能是拟合方法的伪影。作者(S)版权所有。2008年英国皇家经济学会会刊编辑
Motivated by finance applications, we assessed the performance of several univariate density estimation methods, focusing on their ability to deal with heavy-tailed target densities. Four approaches, a fixed bandwidth kernel estimator, an adaptive bandwidth kernel estimator, the Hermite series (SNP) estimator of Gallant and Nychka, and the logspline estimator of Kooperberg and Stone, are compared. We conclude that the logspline and adaptive kernel methods provide superior performance, and the convergence rate of the SNP estimator is remarkably slow compared with the other methods. The Hellinger convergence rate of the SNP estimator is derived as a function of tail heaviness. These findings are confirmed in Monte Carlo experiments. Qualitative assessment reveals the possibility that side lobes in the tails of the fixed kernel and SNP estimates are artefacts of the fitting method. Copyright The Author(s). Journal compilation Royal Economic Society 2008