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Generalised Wald Type Test of Nonlinear Restrictions

DOI: 10.4236/oalib.1103923, PP. 1-8

Subject Areas: Statistics And Econometrics

Keywords: Nonlinear Restrictions, Deficient Rank, Singular Covariance Matrix, Generalised Wald Test

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This paper proposes a generalised Wald type tests to test the hypothesis of the nonlinear restrictions. We circumvent the problem of singularity of the covariance matrix associated with the usual Wald test by proposing a generalised inverse procedure, and an alternative simple procedure which can be approximated by a suitable chi-square distribution. New threshold value is derived to estimate the rank of the covariance matrix.

Cite this paper

Ratsimalahelo, Z. (2017). Generalised Wald Type Test of Nonlinear Restrictions. Open Access Library Journal, 4, e3923. doi:


[1]  Sargan, J.D. (1980) Some Tests of Dynamic Specification for a Single Equation. Econometrica, 48, 879-898.
[2]  Gregory, A.W. and Veall, M.R. (1985) Formulating Wald Tests of Nonlinear Restrictions. Econometrica, 53, 1465-1468.
[3]  Gregory, A.W. and Veall, M.R. (1986) Wald Tests of Common Factor Restrictions. Economics Letters, 22, 203-208.
[4]  Andrew, D.W.K. (1987) Asymptotic Results for Generalized Wald Tests. Econometric Theory, 3, 348-358.
[5]  Toda, H.Y. and Phillips, P.C.B. (1993) Vector Autoregression and Causality. Econometrica, 59, 229-255.
[6]  Lütkepohl, H. and Burda (1997) Modified Wald Tests under Nonregular Conditions. Journal of Econometrics, 78, 315-332.
[7]  Lütkepohl, H. (1993) Introduction to Multiple Time Series Analysis. 2nd Edition, Springer, Berlin.
[8]  Johansen, S. (1995) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press, Oxford.
[9]  Gallant, A.R. (1977) Testing a Nonlinear Regression Specification: A Nonregular case. Journal of American Statistical Association, 72, 523-530.
[10]  Ratsimalahelo, Z. (2001) Specification of VARMA Echelon Form Models. In: Neck, R. Eds., Proceedings IFAC in Symposium on Modelling and Control of Economic Systems, Elsevier, Pergamon Press, 129-137.
[11]  Wilkinson, W.H. (1965) Algebraic Eigenvalue Problems. Oxford University Press, Oxford.
[12]  Ratsimalahelo, Z. (2003) Strongly Consistent Determination of the Rank of Matrix. Working Paper, University of Franche-Comté, U.F.R Sciences Economiques.
[13]  Lardies, J. and Ratsimalahelo, Z. (2005) Model Order Estimation of Multivariable Stochastic Process. Communications in Statistics-Simulation and Computation, 34, 863-877.


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