Event(s) on April 2023

• Tuesday, 18th April, 2023

  Title:	Normal-Reference Tests for High-Dimensional Hypothesis Testing
  Speaker:	Professor Jin-Ting Zhang, Department of Statistics and Data Science, National University of Singapore
  Time/Place:	16:00  -  17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	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.

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