张金廷（张金廷新加坡国立大学）

暨南经院学术系列活动之

名师讲座系列第103期

主题：Normal-Reference Tests for High-Dimensional Hypothesis Testing

主讲人：张金廷 新加坡国立大学

主持人：王国长 暨南大学

时间：2024年12月18日（周三）上午9:30-10:30

地点：暨南大学石牌校区经济学院大楼（中惠楼）503室

In the past two decades, much attention has been paid for high-dimensional hypothesis testing.Several centralized or non-centralized L2-norm based test statistics have been proposed.Most of them imposed strong assumptions on the underlying covariance structure of the high-dimensional data so that the associated test statistics are asymptotically normally distributed. In real data analysis,however, these assumptions are hardly checked so that the resulting tests have a size control problem when the required assumptions are not satisfied.To overcome this difficulty,in this talk, we investigate a so-called normal-reference test which can control the size well.In the normal-reference test,the null distribution of a test statistic is approximated with that of a chi-square-type mixture which is obtained from the test statistic when the null hypothesis holds and when the samples are normally distributed. The distribution of the chi-square-type mixture can be well approximated by a three-cumulant matched χ2-approximation with the approximation parameters consistently estimated from the data.Two simulation studies demonstrate that in terms of size control,the proposed normal- reference test performs well regardless of whether the data are nearly uncorrelated, moderately correlated,or highly correlated and it performs much better than two existing competitors. A real data example illustrates the proposed normal-reference test.