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Multivariate Hermite polynomials and information matrix tests

Dante Amengual, Gabriele Fiorentini () and Enrique Sentana ()

No 2021_07, Econometrics Working Papers Archive from Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti"

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)
Pages: 22 pages
Date: 2021-05
New Economics Papers: this item is included in nep-ore
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Working Paper: Multivariate Hermite polynomials and information matrix tests (2021) Downloads
Working Paper: Multivariate Hermite polynomials and information matrix tests (2021) Downloads
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