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Deriving Tests of the Semi-Linear Regression Model Using the Density Function of a Maximal Invariant


  • Jahar L. Bhowmik


  • Maxwell L. King



In the context of a general regression model in which some regression coefficients are of interest and others are purely nuisance parameters, we derive the density function of a maximal invariant statistic with the aim of testing for the inclusion of regressors (either linear or non-linear) in linear or semi-linear models. This allows the construction of the locally best invariant test, which in two important cases is equivalent to the one-sided t-test for a regression coefficient in an artificial linear regression model.

Suggested Citation

  • Jahar L. Bhowmik & Maxwell L. King, 2005. "Deriving Tests of the Semi-Linear Regression Model Using the Density Function of a Maximal Invariant," Monash Econometrics and Business Statistics Working Papers 19/05, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2005-19

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    References listed on IDEAS

    1. Wu, P.X. & King, M.L., 1994. "One Sided Hypothesis Testing in Econometrics: A Survey," Monash Econometrics and Business Statistics Working Papers 6/94, Monash University, Department of Econometrics and Business Statistics.
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    More about this item


    Invariance; linear regression model; locally best invariant test; non-linear regression model; nuisance parameters; t-test.;

    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

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