COMMON FUNCTIONAL PRINCIPAL COMPONENTS
COMMON FUNCTIONAL PRINCIPAL COMPONENTS
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DOI：
10.1214/07-aos516
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发表时间：
2009-02-01
影响因子：
4.5
通讯作者：
Kneip, Alois
中科院分区：
文献类型：
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作者：
Benko, Michal;Haerdle, Wolfgang;Kneip, Alois
基于Karhunen-Loeve 分解的函数主成分分析（FPCA）已成功应用于许多应用中，主要针对单样本问题。在本文中，我们考虑两个示例问题的共同函数主成分。我们的研究不仅受到这种数据情况的理论挑战的推动，而且还受到隐含波动率（IV）函数动态的实际问题的推动。对于不同的期限，IV 的对数回报是（平滑）随机函数的样本，这里提出的方法研究它们随机行为的相似性。首先，我们提出了一种从离散噪声数据估计功能主成分的新方法。接下来我们提出 FPCA 的二样本推理并发展二样本理论。我们提出了自举测试来测试两个功能样本的特征值、特征函数和均值函数的相等性，通过模拟研究说明测试特性，并将该方法应用于电视分析。
Functional principal component analysis (FPCA) based on the Karhunen-Loeve decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation, but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the log-returns of IVs are samples of (smooth) random functions and the methods proposed here study the similarities of their stochastic behavior. First we present a new method for estimation of functional principal components from discrete noisy data. Next we present the two sample inference for FPCA and develop the two sample theory. We propose bootstrap tests for testing the equality of eigenvalues, eigenfunctions, and mean functions of two functional samples, illustrate the test-properties by simulation study and apply the method to the TV analysis.