Journal of Statistical Theory and Practice

, Volume 6, Issue 2, pp 251–259 | Cite as

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

  • Jahar L. BhowmikEmail author
  • 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 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.

AMS Subject Classification

91G70 62H10 


Invariance Linear regression model Locally best invariant test Nonlinear regression model Nuisance parameters t-test 


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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Faculty of Life and Social SciencesSwinburne University of TechnologyMelbourneAustralia
  2. 2.Department of Econometrics and Business StatisticsMonash UniversityMelbourneAustralia

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