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Invariance, Nonlinear Models, and Asymptotic Tests

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Author Info
Dagenais, Marcel G
Dufour, Jean-Marie

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Abstract

The invariance properties of several asymptotic tests are studied: invariance to hypothesis representation, reparameterization, and rescaling. Noninvariant tests include Wald tests, variants of LM tests, and Neyman's C(" alpha") tests. For all these tests, simply changing measurement units can lead to vastly different results, e.g. in models with Box-Cox transformations. Various consistent estimators of the information matrix produce tests with different invariance properties. Sufficient conditions are established under which a generalized C(" alpha") test becomes invariant to hypothesis reformulations, reparameterizations, and rescaling. In many practical cases, invariant C(" alpha") tests are much cheaper to compute than other invariant tests (e.g., LR tests). Copyright 1991 by The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 59 (1991)
Issue (Month): 6 (November)
Pages: 1601-15
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Handle: RePEc:ecm:emetrp:v:59:y:1991:i:6:p:1601-15

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  1. Jean-Marie Dufour & Alain Trognon, 2000. "Invariant Tests Based on M-Estimators, Estimating Functions and the Generalized Method of Moments," Econometric Society World Congress 2000 Contributed Papers 1420, Econometric Society. [Downloadable!]
  2. N.E. Savin & Allan H. Wuertz, . "The Effect of Nuisance Parameters on Size and Power; LM Tests in Logit Models," Economics Working Papers 1997-17, School of Economics and Management, University of Aarhus. [Downloadable!]
  3. Marcos A. Rangel & Duncan Thomas, 2006. "Out of West Africa: Evidence on the Efficient Allocation of Resources within Farm Households," Working Papers 0515, Harris School of Public Policy Studies, University of Chicago. [Downloadable!]
  4. JOUNEAU-SION, FrŽdŽric & TORRES, Olivier, 2000. "Auctions with discrete increments: a structural econometric approach based on dominated strategies," CORE Discussion Papers 2000046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  5. Michael Lechner, 1999. "An Evaluation of Public-Sector-Sponsored Continuous Vocational Training Programs in East Germany," IZA Discussion Papers 93, Institute for the Study of Labor (IZA). [Downloadable!]
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  6. Jean-Marie Dufour & Joanna Jasiak, 2000. "Finite Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors," Econometric Society World Congress 2000 Contributed Papers 1536, Econometric Society. [Downloadable!]
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  7. Erdenebat Bataa & Dong H. Kim & Denise R. Osborn, 2006. "A Further Examination of the Expectations Hypothesis for the Term Structure," The School of Economics Discussion Paper Series 0611, Economics, The University of Manchester. [Downloadable!]
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  8. Dong, Fengxia & Fuller, Frank, 2004. "Testing For Separability And Structural Change In Urban Chinese Food Demand," 2004 Annual meeting, August 1-4, Denver, CO 19923, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  9. Emma M. Iglesias & Garry D.A. Phillips, 2004. "Multivariate Arch Models: Finite Sample Properties Of Ml Estimators And An Application To An Lm-Type Test," Working Papers. Serie AD 2004-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  10. N.E. Savin & Allan Wurtz, 1996. "The Effect of Nuisance Parameters on the Power of LM Tests in Logit and Probit Models," Econometrics 9606002, EconWPA. [Downloadable!]
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  11. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics. [Downloadable!]
  12. Khalaf, Lynda & Saphores, Jean-Daniel & Bilodeau, Jean-François, 2000. "Simulation-Based Exact Tests with Unidentified Nuisance Parameters Under the Null Hypothesis: the Case of Jumps Tests in Models with Conditional Heteroskedasticity," Cahiers de recherche 0004, GREEN. [Downloadable!]
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  13. Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, Economics Bulletin, vol. 3(62), pages 1-10. [Downloadable!]
  14. Christian Gourieroux & Alain Monfort & Eric Renault, 1993. "Tests sur le noyau, l'image et le rang de la matrice des coefficients d'un modéle linéaire multivarié," Annales d'Economie et de Statistique, ADRES, issue 32, pages 05, Octobre-D. [Downloadable!]
  15. Michael Lechner, 1999. "The Effects of Enterprise-Related Training in East Germany on Individual Employment and Earnings," Annales d'Economie et de Statistique, ADRES, issue 55-56, pages 05, Juillet-D. [Downloadable!]
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