English

An invariant modification of the bilinear form test

Statistics Theory 2026-02-06 v1 Econometrics Statistics Theory

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.

Keywords

Cite

@article{arxiv.2602.05592,
  title  = {An invariant modification of the bilinear form test},
  author = {Angelo Garate and Felipe Osorio and Federico Crudu},
  journal= {arXiv preprint arXiv:2602.05592},
  year   = {2026}
}

Comments

7 pages