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Multivariate Hermite polynomials and information matrix tests

Author

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  • Amengual, Dante
  • Fiorentini, Gabriele
  • Sentana, Enrique

Abstract

The information matrix test for a normal random vector is shown to coincide with the sum of the moment tests for all third- and fourth-order multivariate Hermite polynomials. The statistic is decomposed as the sum of the marginal information matrix test for a subvector, the conditional information matrix test for the complementary subvector, and a third leftover component. It is also shown that exact finite sample distributions can be obtained by drawing spherical Gaussian vectors and orthogonalising them using sample moments. These tests are applied to assess the implications of Gibrat’s law for US city sizes using the three most recent censuses.

Suggested Citation

  • Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2026. "Multivariate Hermite polynomials and information matrix tests," Econometrics and Statistics, Elsevier, vol. 39(C), pages 22-48.
    • Handle: RePEc:eee:ecosta:v:39:y:2026:i:c:p:22-48
    DOI: 10.1016/j.ecosta.2024.01.005
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    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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