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An invariant modification of the bilinear form test

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  • Angelo Garate
  • Felipe Osorio
  • Federico Crudu

Abstract

The invariance properties of certain likelihood-based asymptotic tests as well as their extensions for M-estimation, estimating functions and the generalized method of moments have been well studied. The simulation study reported in Crudu and Osorio [Econ. Lett. 187: 108885, 2020] shows that the bilinear form test is not invariant to one-to-one transformations of the parameter space. This paper provides a set of suitable conditions to establish the invariance property under reparametrization of the bilinear form test for linear or nonlinear hypotheses that arise in extremum estimation which leads to a simple modification of the test statistic. Evidence from a Monte Carlo simulation experiment suggests good performance of the proposed methodology.

Suggested Citation

  • Angelo Garate & Felipe Osorio & Federico Crudu, 2026. "An invariant modification of the bilinear form test," Papers 2602.05592, arXiv.org.
    • Handle: RePEc:arx:papers:2602.05592
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    References listed on IDEAS

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