摘要：In this paper, we propose a nonparametric independence test based on mutual information. Distinguished from the previous work, we estimate the mutual information in a conditional density form, whose dimension could be reduced to 1 with new projection methods. The optimal projection direction, which we name as maximum unit direction, is estimated by maximizing a penalized mutual information. An independence test is later on carried out via the newly estimated mutual information and is shown to be insensitive to the dimensions. The test is consistent against fixed alternatives, and can detect local alternatives at a fast rate almost as if the model was univariate. Numerical results indicate that the test is more powerful compared with other existing independence tests, especially when the sample size is small or the dimension is large.
报告人简介: 郭旭，现为北京师范大学统计学院副教授，博士生导师。2014年获得香港浸会大学博士学位。郭旭自2018年9月至2020年2月作为助理研究教授(Assistant Research Professor)访问美国宾州州立大学统计系。郭旭一直从事模型设定检验、高维数据分析和半参数回归分析等方面的研究，并取得了一系列的研究成果。