Abstract
In this paper, we use a maximal invariant likelihood (MIL) to construct two likelihood ratio (LR) tests in the context of a semi-linear regression model. The first involves testing for the inclusion of a non-linear regressor and the second involves testing a linear regressor against the alternative of a non-linear regressor. We report the results of a Monte Carlo experiment that compares the size and power properties of the traditional LR tests with those of our proposed MIL based LR tests. Our simulation results show that in both cases, the MIL based tests have more accurate asymptotic critical values and better behaved (i.e., better centred) power curves than their classical counterparts.
Similar content being viewed by others
References
Amemiya, T., Advanced Econometrics (Harvard University Press, Cambridge, 1985).
Anderson, E.B., Asymptotic properties of conditional maximum-likelihood estimators, Journal of the Royal Statistical Society B, 32, (1970), 283–302.
Ara, I., Marginal Likelihood Based Tests of Regression Disturbances, unpublished Ph.D. thesis (Monash University, Clayton, Melbourne, 1995).
Bellhouse, D.R., Marginal and approximate conditional likelihoods for sampling on successive occasions. Survey Methodology, 17, (1991), 69–78.
Bhowmik, J.L. and King M.L., Parameter estimation in linear models with a non-linear component using a maximal invariant likelihood function, paper presented at the 2002 Australasian Meeting of the Econometric Society, Brisbane, Australia (2002).
Bhowmik, J.L. and King M.L., Parameter estimation in semilinear models using a maximal invariant likelihood function, Department of Econometrics and Business Statistics, working paper 18/05, Monash University, Australia (2005), web address: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2005/.
Breusch, T.S. and Schmidt, P., Alternative forms of the Wald test: How long is a piece of string? Communications in Statistics, A 7, (1988), 2789–2795.
Corduas, M., The Use of Marginal Likelihood in Testing for Correlation in Time Series Regression, unpublished M. Phil. thesis, (University of Lancaster, 1986).
Cox, D.R. and Hinkley, D.V., Theoretical Statistics (Chapman and Hall, London, 1974).
Dobler, C.P., The one-way layout with ordered parameters: A survey of advances since 1988, Journal of Statistical Planning and Inference, 107, (2002) 75–88.
Gallant, A.R., Non-linear regression, The American Statistician, 29, (1975), 75–81.
GAUSS, GAUSS for Windows NT/95 Version 3.2.35 (Aptech Systems, Inc., Maple Valley, W.A., 1998)
Godfrey, L.G., Misspecification Tests in Econometrics: The Lagrange Multiplier Principle and Other Approaches (Cambridge University Press, Cambridge, 1988).
Greene, W.H., Econometric Analysis (Prentice Hall, New York, 1997).
King, M.L., Robust tests for spherical symmetry and their application to least squares regression, The Annals of Statistics, 8 (1980), 1265–1271.
King, M.L., Testing for autocorrelation in linear regression models: A survey, in Specification Analysis in the Linear Model, M.L. King and D.E.A. Giles (eds.), Routledge and Kegan Paul, London, (1987), 19–73.
Konstas, P. and Khouja, M.W., The Keynesian demand-for-money function: Another look and some additional evidence, Journal of Money, Credit and Banking, 1, (1969), 765–777.
Laskar, M.R., Estimation and Testing of Linear Regression Disturbances Based on Modified Likelihood and Message Length Functions, unpublished Ph.D. thesis, Monash University, Clayton, Melbourne, (1998).
Laskar, M.R. and King, M.L., Modified Wald test for regression disturbances, Economic Letters, 56, (1997), 5–11.
Laskar, M.R. and King, M.L., Estimation and testing of regression disturbances based on modified likelihood functions, Journal of Statistical Planning and Inference, 71, (1998), 75–92.
Laskar, M.R. and King, M.L., Modified likelihood and related methods for handling nuisance parameters in the linear regression model, in A.K.M.E. Saleh ed. Data Analysis from Statistical Foundations, Nova Science Publisher, Inc. Huntington, New York, (2001), 119–142.
McManus, D.A., Nankervis, J.C. and Savin, N.E., Multiple optima and asymptotic approximations in the partial adjustment model, Journal of Econometrics, 62, (1994), 91–128.
Moulton, B.R. and Randolph, W.C., Alternative tests of the error components model, Econometrica, 57, (1989), 685–693.
Mukherjee, R., Comparison between the conditional likelihood ratio and the usual likelihood ratio tests, Journal of the Royal Statistical Society, B, 54, (1992), 189–194.
Mukherjee, R., Conditional likelihood and power: Higher order asymptotics, Proceedings of the Royal Society of London, A, 438, (1992), 433–446.
Neyman, J. and Scott, E.L., Consistent estimates based on partially consistent observations, Econometrica, 16, (1948), 1–32.
Rahman, S. and King, M.L., A comparison of marginal likelihood based and approximate point optimal tests for random regression coefficients in the presence of autocorrelation, Pakistan Journal of Statistics, 10, (1994), 375–394.
Rahman, S. and King, M.L., Marginal likelihood score based tests of regression disturbances in the presence of nuisance parameters, Journal of Econometrics, 82, (1998), 81–106.
Shephard, N., Maximum likelihood estimation of regression models with stochastic trend components. Journal of the American Statistical Association, 88, (1993), 590–595.
Tunnicliffe Wilson, G., On the use of marginal likelihood in time series model estimation, Journal of the Royal Statistical Society, B, 51, (1989), 15–27.
Wolfram, S., Mathematica: A System for Doing Mathematics by Computer, (Addison-Wesley Publishing Company, 2nd edition, New York, 1993).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bhowmik, J.L., King, M.L. Maximal invariant likelihood based testing of semi-linear models. Statistical Papers 48, 357–383 (2007). https://doi.org/10.1007/s00362-006-0342-7
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00362-006-0342-7