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首页> 外文期刊>Journal of Multivariate Analysis: An International Journal >Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas
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Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas

机译：简化藤蔓copulas在非参数密度估计中规避维度的诅咒

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摘要

Practical applications of nonparametric density estimators in more than three dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as dimension increases. We show that one can evade the curse of dimensionality by assuming a simplified vine copula model for the dependence between variables. We formulate a general nonparametric estimator for such a model and show under high-level assumptions that the speed of convergence is independent of dimension. We further discuss a particular implementation for which we validate the high-level assumptions and establish asymptotic normality. Simulation experiments illustrate a large gain in finite sample performance when the simplifying assumption is at least approximately true. But even when it is severely violated, the vine copula based approach proves advantageous as soon as more than a few variables are involved. Lastly, we give an application of the estimator to a classification problem from astrophysics. (C) 2016 Elsevier Inc. All rights reserved.
机译：非参数密度估计器在超过三个维度上的实际应用遭受了众所周知的维度诅咒的困扰：随着维度的增加，收敛变慢。我们表明，可以通过假设简化的藤蔓copula模型来变量之间的依赖性来逃避维数的诅咒。我们为这种模型制定了一个通用的非参数估计量，并在高级假设下证明了收敛速度与维数无关。我们将进一步讨论一个特定的实现，为此我们可以验证高级假设并建立渐近正态性。仿真实验表明，当简化假设至少近似为真时，有限样本性能将大幅度提高。但是，即使严重违反了该规则，只要涉及多个变量，基于葡萄树copula的方法就被证明是有利的。最后，我们将估算器应用于天体物理学的分类问题。 （C）2016 Elsevier Inc.保留所有权利。

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