IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2005-18.html
   My bibliography  Save this paper

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

Author

Listed:
  • Jahar L. Bhowmik
  • Maxwell L. King

Abstract

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.

Suggested Citation

  • Jahar L. Bhowmik & Maxwell L. King, 2005. "Parameter Estimation in Semi-Linear Models Using a Maximal Invariant Likelihood Function," Monash Econometrics and Business Statistics Working Papers 18/05, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2005-18
    as

    Download full text from publisher

    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp18-05.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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 765-777, November.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jahar Bhowmik & Maxwell King, 2007. "Maximal invariant likelihood based testing of semi-linear models," Statistical Papers, Springer, vol. 48(3), pages 357-383, September.
    2. Badi Baltagi & Seuck Heun Song & Byoung Cheol Jung, 2002. "Simple Lm Tests For The Unbalanced Nested Error Component Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 167-187.
    3. Sriananthakumar, Sivagowry, 2013. "Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach," Economic Modelling, Elsevier, vol. 33(C), pages 126-136.
    4. Baltagi, Badi H. & Li, Qi, 1995. "Testing AR(1) against MA(1) disturbances in an error component model," Journal of Econometrics, Elsevier, vol. 68(1), pages 133-151, July.
    5. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    6. Silvapulle, Paramsothy & King, Maxwell L., 1993. "Nonnested testing for autocorrelation in the linear regression model," Journal of Econometrics, Elsevier, vol. 58(3), pages 295-314, August.
    7. Dastoor, Naorayex K. & Fisher, Gordon, 1988. "On Point-Optimal Cox Tests," Econometric Theory, Cambridge University Press, vol. 4(1), pages 97-107, April.
    8. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.
    9. 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.
    10. Atukorala, Ranjani & Sriananthakumar, Sivagowry, 2015. "A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information," Economic Modelling, Elsevier, vol. 45(C), pages 169-174.
    11. Martellosio, Federico, 2008. "Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression," MPRA Paper 7255, University Library of Munich, Germany.
    12. Laskar, Mizan R. & King, Maxwell L., 1997. "Modified Wald test for regression disturbances," Economics Letters, Elsevier, vol. 56(1), pages 5-11, September.
    13. J Mur, 1999. "Testing for Spatial Autocorrelation: Moving Average versus Autoregressive Processes," Environment and Planning A, , vol. 31(8), pages 1371-1382, August.
    14. Marc K. Francke & Siem Jan Koopman & Aart F. De Vos, 2010. "Likelihood functions for state space models with diffuse initial conditions," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 407-414, November.
    15. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    16. Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.
    17. Jae Kim & Mahbuba Yeasmin, 2005. "The Size and Power of the Bias-Corrected Bootstrap Test for Regression Models with Autocorrelated Errors," Computational Economics, Springer;Society for Computational Economics, vol. 25(3), pages 255-267, June.
    18. Willa W. Chen & Rohit S. Deo, 2009. "The restricted likelihood ratio test at the boundary in autoregressive series," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 618-630, November.
    19. Philip A. Shively, 2001. "Trend-stationary GNP: evidence from a new exact pointwise most powerful invariant unit root test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 537-551.
    20. Sriananthakumar, Sivagowry & King, Maxwell L., 2006. "A new approximate point optimal test of a composite null hypothesis," Journal of Econometrics, Elsevier, vol. 130(1), pages 101-122, January.

    More about this item

    Keywords

    Maximum likelihood estimation; nonlinear modelling; simulation experiment; two-step estimation.;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2005-18. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.