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Mixed LR-$C(α)$-type tests for irregular hypotheses, general criterion functions and misspecified models

Jean-Marie Dufour, Purevdorj Tuvaandorj

arXiv 20 Oct 2025 · Econometrics

arXiv:2510.17070 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper introduces a likelihood ratio (LR)-type test that possesses the robustness properties of \(C(α)\)-type procedures in an extremum estimation setting. The test statistic is constructed by applying separate adjustments to the restricted and unrestricted criterion functions, and is shown to be asymptotically pivotal under minimal conditions. It features two main robustness properties. First, unlike standard LR-type statistics, its null asymptotic distribution remains chi-square even under model misspecification, where the information matrix equality fails. Second, it accommodates irregular hypotheses involving constrained parameter spaces, such as boundary parameters, relying solely on root-\(n\)-consistent estimators for nuisance parameters. When the model is correctly specified, no boundary constraints are present, and parameters are estimated by extremum estimators, the proposed test reduces to the standard LR-type statistic. Simulations with ARCH models, where volatility parameters are constrained to be nonnegative, and parametric survival regressions with potentially monotone increasing hazard functions, demonstrate that our test maintains accurate size and exhibits good power. An empirical application to a two-way error components model shows that the proposed test can provide more informative inference than the conventional \(t\)-test.

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Andrews, D. W. K (1999) Estimation When a Parameter is on a Boundary0.92843100%
2Ketz, P (2018) Subvector Inference When the True Parameter Vector May Be Near or at the Boundary0.87472100%
3Cavaliere, G., H. B. Nielsen, R. S. Pedersen, and A. Rahbek (2022) Bootstrap Inference on the Boundary of the Parameter Space, with Application to Conditional Volatility Models0.84333100%
4Gouriéroux, C. and A. Monfort (1995) Statistics and Econometric Models, Volumes One and Two0.73732100%
5Silvapulle, M. J. and P. K. Sen (2011) Constrained Statistical Inference: Inequality, Order, and Shape Restrictions, Volume 9120.73732100%
6Andrews, D. W. K (2001) Testing When a Parameter is on the Boundary of the Maintained Hypothesis0.64422100%
7Dufour, J.-M., A. Trognon, and P. Tuvaandorj (2016) Generalized $C()$ Tests in Estimating Functions with Serial Dependence self0.64422100%
8Dufour, J.-M., A. Trognon, and P. Tuvaandorj (2017) Invariant Tests Based on M-Estimators, Estimating Functions, and the Generalized Method of Moments self0.64422100%
9Francq, C. and J.-M. Zakoian (2019) GARCH Models: Structure, Statistical Inference and Financial Applications0.64422100%
10Newey, W. K. and D. McFadden (1994) Large Sample Estimation and Hypothesis Testing0.64422100%

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