Department of Economics
Texas A&M University
“Improved Inference on the Rank of a Matrix”
This paper develops new methods for examining a “no greater than” inequality of the rank of a matrix and for rank determination in a general setup, which improve upon existing methods. Existing rank tests assume a priori that the rank is no less than the hypothesized value, which is often unrealistic. These tests when directly applied may fail to control the asymptotic null rejection rate, and the multiple testing method based on them can be conservative with the asymptotic null rejection rate strictly below the nominal level whenever the rank is less than the hypothesized value. We prove that our proposed tests have the asymptotic null rejection rate that is exactly equal to the nominal level under minimal assumptions regardless of whether the rank is less than or equal to the hypothesized value. As our simulation results show, these characteristics lead to an improved power property in general. In application to a context with stationary and nonstationary data, respectively, our tests yield improved tests for identification in linear IV models and for the existence of stochastic trend and/or cointegration with or without VAR specification. In addition, our simulation results show that the improved power property of our tests leads to an improved accuracy of the sequential testing procedure for rank determination.
Joint work with Qihui Chen.
Friday, 9/8/2017, BLOC 113, 11:30 am