Multivariate Hermite polynomials and information matrix tests

• Dante Amengual ^[1] ; Gabriele Fiorentini ^[2] ; Enrique Sentana ^[1]
  1. [1] Centro de Estudios Monetarios y Financieros (CEMFI)
  2. [2] Università di Firenze
• Localización: Documentos de Trabajo ( CEMFI ), Nº. 3 (CEMFI Working Paper No. 2103, May 2021), 2021
• Idioma: inglés
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• Resumen

  • 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.