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Hypothesis Testing in High-Dimensional Linear Regression:
Assoc Prof Zhang Jin-Ting
Department of Statistics and Applied Probability, NUS
Wednesday 01 November 2017, 03:00pm - 04:00pm
S16-06-118, DSAP Seminar Room

In this talk, we consider a general linear hypothesis testing (GLHT) problem in high-dimensional linear regression where the data dimension may be much larger than the sample size. Recently, several non-scale and scale-invariant tests have been proposed for this important  GLHT problem which includes one-way and two-way MANOVA tests as special cases.  Most of these tests  impose strong assumptions on the underlying covariance matrix so that their test statistics are asymptotically normally distributed. However, a simulation example and some theoretical justifications indicate that  these assumptions may not be satisfied or hardly be checked so that these tests may not be able to maintain the nominal  size well in practice. Some scale-invariant tests  employ a so-called adjustment coefficient to improve the convergence of their test statistics to normal distributions.  However, it turns out that  this  adjustment coefficient  works well in improving the convergence of a scale-invariant test to a normal distribution when the underlying null distribution of the test is approximately  normal but  it substantially worsens the size control and power of the test otherwise. To overcome these problems, in this talk, we propose a simple and adaptive scale-invariant test which has good size control and power  without imposing strong assumptions on the  underlying covariance or correlation matrix. In addition, we adopt a strategy to employ the adjustment coefficient smartly to the proposed test. Simulation  and  real data examples  demonstrate the good performance of the proposed test in terms of size control and power, via comparing it  against several non-scale  and scale-invariant tests.

Joint work with Liang Zhang, Tianming Zhu, and Jin-Ting Zhang.