Kernel-Based Partial Permutation Test for Detecting Heterogeneous Functional Relationship
Kernel-Based Partial Permutation Test for Detecting Heterogeneous Functional Relationship
复制标题
用于检测异质函数关系的基于内核的部分排列测试
DOI：
10.1080/01621459.2021.2000867
复制
发表时间：
2023
影响因子：
3.7
通讯作者：
Liu, Jun S.
中科院分区：
文献类型：
--
作者：
Li, Xinran;Jiang, Bo;Liu, Jun S.
提出了一种基于核的部分置换检验方法，用于检验不同群体间响应与协变量之间的函数关系是否相等。其主要思想直观且易于实现，即保持核矩阵的响应向量和主要主分量的投影固定，并改变其在其余主分量上的投影。提出的检验允许不同的核选择，对应于零假设下不同类别的函数。首先，使用线性或多项式核，我们的部分置换检验在有限样本中对高斯噪声的线性或多项式回归模型完全有效；类似的结果可以直接推广到具有有限特征空间的核。其次，通过允许内核特征空间随样本大小发散，测试可以对更广泛的函数类具有大样本有效性。第三，对于可能具有无限维特征空间的一般核，当协变量在所有组中完全平衡时，部分置换检验是完全有效的，或者当底层函数遵循某些正则化高斯过程时，部分置换检验是渐近有效的。我们进一步建议使用两个（嵌套的）高斯过程回归模型之间的似然比来检验统计量，并提出利用EM算法和牛顿方法的计算效率高的算法，其中牛顿方法还涉及Fisher评分和二次规划，当EM收敛缓慢时特别有用。对相关噪声和非高斯噪声的扩展也进行了理论和数值研究。此外，测试可以扩展为同时使用多个内核，从而可以享受每个内核的属性。仿真研究和实际应用都证明了该测试方法的有效性。
We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the projections of the response vectorYon leading principle components of a kernel matrix fixed and permuteY’s projections on the remaining principle components. The proposed test allows for different choices of kernels, corresponding to different classes of functions under the null hypothesis. First, using linear or polynomial kernels, our partial permutation tests are exactly valid in finite samples for linear or polynomial regression models with Gaussian noise; similar results straightforwardly extend to kernels with finite feature spaces. Second, by allowing the kernel feature space to diverge with the sample size, the test can be large-sample valid for a wider class of functions. Third, for general kernels with possibly infinite-dimensional feature space, the partial permutation test is exactly valid when the covariates are exactly balanced across all groups, or asymptotically valid when the underlying function follows certain regularized Gaussian processes. We further suggest test statistics using likelihood ratio between two (nested) Gaussian process regression models, and propose computationally efficient algorithms utilizing the EM algorithm and Newton’s method, where the latter also involves Fisher scoring and quadratic programming and is particularly useful when EM suffers from slow convergence. Extensions to correlated and non-Gaussian noises have also been investigated theoretically or numerically. Furthermore, the test can be extended to use multiple kernels together and can thus enjoy properties from each kernel. Both simulation study and application illustrate the properties of the proposed test.
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DOI：
10.1093/oxfordhb/9780198794219.013.12
发表时间：
2019
期刊：
The Oxford Handbook of Management Ideas
影响因子：
--
作者：
M. Barros;Charles
通讯作者：
Charles
DOI：
10.1080/01621459.1984.10477069
发表时间：
1984-03
影响因子：
3.7
作者：
D. Freedman;S. Peters
通讯作者：
D. Freedman;S. Peters
非参数测试的提前停止
DOI：
--
发表时间：
2018
期刊：
Proceedings of the 32nd International Conference on Neural Information Processing
影响因子：
--
作者：
Liu, M.;Cheng, G.
通讯作者：
Cheng, G.
DOI：
10.1111/j.2517-6161.1977.tb01600.x
发表时间：
1977-01-01
期刊：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL
影响因子：
--
作者：
DEMPSTER, AP;LAIRD, NM;RUBIN, DB
通讯作者：
RUBIN, DB
影响因子：
0.9
作者：
Branson, Zach;Rischard, Maxime;Miratrix, Luke W.
通讯作者：
Miratrix, Luke W.