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Testing the equality of two positive-definite matrices with application to information matrix testing. (English) Zbl 1453.62277
Chang, Yoosoon (ed.) et al., Essays in honor of Peter C. B. Phillips. Bingley: Emerald. Adv. Econom. 33, 491-556 (2014).
Summary: We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. [the second author, Econometrica 50, 1–25 (1982; Zbl 0478.62088); Estimation, inference, and specification analysis. Cambridge: Cambridge Univ. Press (1994; Zbl 0860.62100)]). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by J. L. Horowitz [“Bootstrap-based critical values for the information matrix test”, J. Econom. 61, No. 2, 395–411 (1994; doi:10.1016/0304-4076(94)90092-2)] delivers critical values that provide admirable level behavior, even in samples as small as $$n=50$$. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.
For the entire collection see [Zbl 1310.62005].
##### MSC:
 62B10 Statistical aspects of information-theoretic topics 62F03 Parametric hypothesis testing 15A18 Eigenvalues, singular values, and eigenvectors
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