Angelo Garate, Felipe Osorio, Federico Crudu
arXiv 5 Feb 2026 · Mathematics — Statistics Theory
arXiv:2602.05592 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Crudu, F., Osorio, F (2020) Bilinear form test statistics for extremum estimation self | 1.000 | 6 | 4 | 100% |
| 2 | Dufour, J.-M., Trognon, A., Tuvaandorj, P (2017) Invariant test based on $M$-estimators, estimating functions, and generalized method of moments | 1.000 | 6 | 3 | 100% |
| 3 | Gourieroux, C., Monfort, A (1995) Statistics and Econometrics Models: Testing, Confidence Regions, Model Selection and Asymptotic Theory. Vol. 2 | 0.644 | 2 | 2 | 100% |
| 4 | Newey, W.K., West, K.D (1987) Hypothesis testing with efficient method of moments estimators | 0.644 | 2 | 2 | 100% |
| 5 | Phillips, P.C.B., Park, J.Y (1988) On the formulation of Wald tests of nonlinear restrictions | 0.644 | 2 | 2 | 100% |
| 6 | Goh, K.L., King, M.L (1996) Modified Wald tests for non-linear restrictions: A cautionary tale | 0.511 | 2 | 1 | 100% |
| 7 | Greville, T.N.E (1966) Note on the generalized inverse of a matrix product | 0.511 | 2 | 1 | 100% |
| 8 | Dagenais, M.G., Dufour, J.-M (1991) Invariance, nonlinear models, and asymptotic tests | 0.405 | 1 | 1 | 100% |
| 9 | Gregory, A.W., Veall, M.R (1985) Formulating Wald tests of nonlinear restrictions | 0.405 | 1 | 1 | 100% |
| 10 | Hansen, L (1982) Large sample properties of generalized method of moments estimators | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 19 scored citations.