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Deriving Tests of the Semi—linear Regression Model Using the Density Function of a Maximal Invariant

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Abstract

In the context of a general regression model in which some regression coefficients are of interest and others are purely nuisance parameters, we define 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.We consider a specific semi-linear model to apply the constructed test.

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Authors and Affiliations

  1. Faculty of Life and Social Sciences, Swinburne University of Technology, Melbourne, VIC, 3122, Australia

    Jahar L. Bhowmik

  2. Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia

    Maxwell L. King

Authors
  1. Jahar L. Bhowmik
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  2. Maxwell L. King
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Correspondence to Jahar L. Bhowmik.

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Bhowmik, J.L., King, M.L. Deriving Tests of the Semi—linear Regression Model Using the Density Function of a Maximal Invariant. J Stat Theory Pract 6, 251–259 (2012). https://doi.org/10.1080/15598608.2012.673871

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  • DOI: https://doi.org/10.1080/15598608.2012.673871

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