【学术讲座】Kernel-based Independence Tests for High-dimensional Response Data

发布者:统计与数据科学学院发布时间:2022-06-07浏览次数:10

专家简介:李启寨,中国科学院数学与系统科学研究院研究员,中国科学院大学岗位教授,美国统计学会会士(2020),国际统计学会推选会员(2016),国家优秀青年科学基金获得者(2017)2001年本科毕业于中国科技大学,2006年博士毕业于中国科学院数学与系统科学研究院;研究方向:生物医学统计、复杂数据分析及应用等;发表及接收发表SCI论文100余篇;现任中国数学会常务理事、中国现场统计研究会常务理事等。

报告摘要:Testing independence between high-dimensional response variable and some co-variates is frequently encountered in statistical applications nowadays, and the kernel-based methods have been developed recently. However, the traditional kernel-based methods may suffer from substantial power loss under the situations with moderate to high correlations among responses. In this work, we first propose a set of kernel-based independence tests on the basis of angles between two reproducing kernel Hilbert spaces, and obtain their asymptotical null distributions. Then, we construct two tests including maximal kernel-based independence test (MKIT) and maximin ecient robust test (MERT). Under some regular conditions, we prove that MKIT and MERT asymptotically follow extreme-value type I-Gumbel distribution and normal distribution, respectively. The powers of MKIT and MERT are also investigated.

Extensive simulation studies show that MKIT and MERT are more powerful and robust than many existing procedures over a wide range of situations. Applications to heterogeneous stock mice and prostate cancer pathway data ulteriorly demonstrate the performances of proposed methods.

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