ABSTRACT It is often critical to accurately model the upper tail behaviour of a random process. Nonparametric density estimation methods are commonly implemented as exploratory data analysis techniques for this purpose and can avoid model specification biases implied by using parametric estimators. In particular, kernel-based estimators place minimal assumptions on the data, and provide improved visualisation over scatterplots and histograms. However kernel density estimators can perform poorly when estimating tail behaviour above a threshold, and can over-emphasise bumps in the density for heavy tailed data. We develop a transformation kernel density estimator which is able to handle heavy tailed and bounded data, and is robust to threshold choice. We derive closed form expressions for its asymptotic bias and variance, which demonstrate its good performance in the tail region. Finite sample performance is illustrated in numerical studies, and in an expanded analysis of the performance of global climate models.

中文翻译：

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使用核方法进行探索性数据分析的尾密度估计

摘要 准确地模拟随机过程的上尾行为通常是至关重要的。为此，非参数密度估计方法通常作为探索性数据分析技术实施，并且可以避免使用参数估计量隐含的模型规范偏差。特别是，基于内核的估计器对数据进行了最少的假设，并提供了对散点图和直方图的改进可视化。然而，核密度估计器在估计高于阈值的尾部行为时可能表现不佳，并且可能过分强调重尾数据的密度波动。我们开发了一个转换核密度估计器，它能够处理重尾和有界数据，并且对阈值选择具有鲁棒性。我们推导出其渐近偏差和方差的封闭形式表达式，这证明了它在尾部区域的良好表现。数值研究和对全球气候模型性能的扩展分析说明了有限样本的性能。