Multivariate Hermite polynomials and information matrix tests

Dante Amengual, Gabriele Fiorentini and Enrique Sentana

Working Paper series from Rimini Centre for Economic Analysis

Abstract: We show that the information matrix test for a multivariate normal random vector coincides with the sum of the two moment tests that look at the means of all the different third- and fourth-order multivariate Hermite polynomials, respectively. We also explain how to simulate its exact, parameter-free, finite sample distribution to any desired degree of accuracy for any dimension of the random vector and sample size. Specifically, we exploit the numerical invariance of the test statistic to affine transformations of the observed variables to simulate draws extremely quickly.

Keywords: Exact test; Hessian matrix; Multivariate normality; Outer product of the score (search for similar items in EconPapers)
JEL-codes: C30 C46 C52 (search for similar items in EconPapers)
Date: 2021-05
New Economics Papers: this item is included in nep-ecm and nep-ore
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http://rcea.org/RePEc/pdf/wp21-12.pdf

Related works:
Working Paper: Multivariate Hermite polynomials and information matrix tests (2021)
Working Paper: Multivariate Hermite polynomials and information matrix tests (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:rim:rimwps:21-12

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