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Parameter Estimation in Semi-Linear Models Using a Maximal Invariant Likelihood Function


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  • Jahar L. Bhowmik


  • Maxwell L. King



In this paper, we consider the problem of estimation of semi-linear regression models. Using invariance arguments, Bhowmik and King (2001) have derived the probability density functions of the maximal invariant statistic for the nonlinear component of these models. Using these density functions as likelihood functions allows us to estimate these models in a two-step process. First the nonlinear component parameters are estimated by maximising the maximal invariant likelihood function. Then the nonlinear component, with the parameter values replaced by estimates, is treated as a regressor and ordinary least squares is used to estimate the remaining parameters. We report the results of a simulation study conducted to compare the accuracy of this approach with full maximum likelihood estimation. We find maximising the maximal invariant likelihood function typically results in less biased and lower variance estimates than those from full maximum likelihood.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 18/05.

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Length: 29 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:msh:ebswps:2005-18

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Keywords: Maximum likelihood estimation; nonlinear modelling; simulation experiment; two-step estimation.;

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  1. Konstas, Panos & Khouja, Mohamad W, 1969. "The Keynesian Demand-for-Money Function: Another Look and Some Additional Evidence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 1(4), pages 765-77, November.
  2. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 81-106.
  3. Laskar, M.R. & King, M.L., 1998. "Modified Likelihood and Related Methods for Handling Nuisance Parameters in the Linear Regression Model," Monash Econometrics and Business Statistics Working Papers 5/98, Monash University, Department of Econometrics and Business Statistics.
  4. King, Maxwell L., 1983. "Testing for autoregressive against moving average errors in the linear regression model," Journal of Econometrics, Elsevier, vol. 21(1), pages 35-51, January.
  5. Ara, I. & King, M.L., 1995. "Marginal Likelihood Based Tests of a Subvector of the Parameter Vector of Linear Regression Disturbances," Monash Econometrics and Business Statistics Working Papers 12/95, Monash University, Department of Econometrics and Business Statistics.
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