%0 Journal Article
%T Constructing Locally Best Invariant Tests of the Linear Regression Model Using the Density Function of a Maximal Invariant
%J American Journal of Mathematics and Statistics
%@ 2162-8475
%D 2013
%I 
%R 10.5923/j.ajms.20130301.07
%X In the context of the linear 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 after eliminating the nuisance parameters by the principle of invariance argument. This allows the construction of a range of optimal test statistics including the locally best invariant (LBI) test which is equivalent to the well-known one-sided t-test. The resultant LBI test is also found to be uniformly most powerful invariant (UMPI).
%K Invariance
%K Maximal Invariant Statistic
%K Nuisance Parameters
%K t-Test
%K Uniformly Most Powerful Invariant (UMPI)
%U http://article.sapub.org/10.5923.j.ajms.20130301.07.html