Testing for additivity and joint effects in multivariate nonparametric regression using Fourier and wavelet methods
Testing for additivity and joint effects in multivariate nonparametric regression using Fourier and wavelet methods
复制标题
使用傅里叶和小波方法测试多元非参数回归中的可加性和联合效应
DOI：
10.1023/b:stco.0000035303.24825.b3
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发表时间：
2004
影响因子：
2.2
通讯作者：
T. Sapatinas
中科院分区：
文献类型：
--
作者：
D. Canditiis;T. Sapatinas
本文考虑了多元非参数回归中的加性和联合效应检验问题，其中数据被建模为在d维（d ≥ 2）格点上观测到的未知响应函数的观测值，并被加性高斯噪声污染。我们提出了适用于齐次和非齐次响应函数的加性和联合效应的检验，使用Amato和Antoniadis（2001）以及Amato，Antoniadis和De Feis（2002）最近研究的张量积傅立叶或小波基中扩展的数据的特定结构。通过应用Fan（1996）的自适应Neyman截断和小波阈值处理程序来构造相应的测试，用于测试高维高斯平均值，以得到经验傅立叶和小波系数。因此，渐近正态性的零假设下的检验统计量和相应的权力在一个特定的替代下的下界。我们使用几个模拟的例子来说明所提出的测试的性能，我们在文献中与其他测试进行比较。
We consider the problem of testing for additivity and joint effects in multivariate nonparametric regression when the data are modelled as observations of an unknown response function observed on a d-dimensional (d ≥ 2) lattice and contaminated with additive Gaussian noise. We propose tests for additivity and joint effects, appropriate for both homogeneous and inhomogeneous response functions, using the particular structure of the data expanded in tensor product Fourier or wavelet bases studied recently by Amato and Antoniadis (2001) and Amato, Antoniadis and De Feis (2002). The corresponding tests are constructed by applying the adaptive Neyman truncation and wavelet thresholding procedures of Fan (1996), for testing a high-dimensional Gaussian mean, to the resulting empirical Fourier and wavelet coefficients. As a consequence, asymptotic normality of the proposed test statistics under the null hypothesis and lower bounds of the corresponding powers under a specific alternative are derived. We use several simulated examples to illustrate the performance of the proposed tests, and we make comparisons with other tests available in the literature.