The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?
The distinction between a nominal framework for the three classical statistics and a perceived framework for each classical statistic provides more ways to interpret these statistics, and intuitively explains as well as more easily shows some well-known results. In particular, each classical statistic can be viewed in terms of a length in each of four spaces and, since the classical procedures per se are equivalent in a perceived framework, two statistics are identical if their perceived frameworks are identical. This helps to integrate the normally separately treated issues of a reformulation of a null hypothesis and of locally equivalent alternatives. For example, a Wald statistic is not invariant if a reformulation changes its perceived framework, and an appropriate score statistic is invariant as its perceived framework is unaffected by considering a locally equivalent alternative. [During the thirty-four months this paper was under consideration at The Econometrics Journal, the Editor-in-charge (Professor Stephane Gregoir) did not reply to three (of the author's four) requests about the status of the submission, and provided neither a referee's report nor a first decision. Also, when asked to intervene by the author, the new Managing Editor (Professor Richard J Smith) offered the author the possibility of submitting the paper (as a new submission) to the new editorial regime, at which point, the author withdrew the paper.]
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- Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September.
- Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
- Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-22, September.
- Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-55, December.
- Dagenais, M.G. & Dufour, J.M., 1987.
"Invariance, Nonlinear Models and Asymptotic Tests,"
Cahiers de recherche
8738, Universite de Montreal, Departement de sciences economiques.
- Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-15, November.
- Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(01), pages 63-82, April.
- Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, June.
- Peter C.B. Phillips & Joon Y. Park, 1986.
"On the Formulation of Wald Tests of Nonlinear Restrictions,"
Cowles Foundation Discussion Papers
801, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-83, September.
- Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
- Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-87, October.
- Davidson, Russell & MacKinnon, James G, 1987.
"Implicit Alternatives and the Local Power of Test Statistics,"
Econometric Society, vol. 55(6), pages 1305-29, November.
- Russell Davidson & James G. MacKinnon, 1984. "Implicit Alternatives and the Local Power of Test Statistics," Working Papers 556, Queen's University, Department of Economics.
- Davidson , R. & Mackinnon, J.G., 1985. "Implicit alternatives and the local power of test statistics," CORE Discussion Papers 1985025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-78, May.
- Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826 Elsevier.
- Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
- Godfrey, L G, 1981. "On the Invariance of the Lagrange Multiplier Test with Respect to Certain Changes in the Alternative Hypothesis," Econometrica, Econometric Society, vol. 49(6), pages 1443-55, November.
- Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
- Dastoor, Naorayex K., 2003. "The equality of comparable extended families of classical-type and Hausman-type statistics," Journal of Econometrics, Elsevier, vol. 117(2), pages 313-330, December.
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