ABSTRACT
Let X 1,…, X n be a sample from density f(x| θ) where θ ⊂ Θ ⊂ ℝ k . The likelihood ratio test provides a general method for testing H 0: θ ∈ Θ0 versus H 1. θ ∈ Θ − Θ0 for a given subset Θ0 of Θ. This tests rejects H 0 when the likelihood ratio test statistic, () https://www.w3.org/1998/Math/MathML"> λ n = sup θ ∈ Θ 0 ∏ 1 n f ( x j | θ ) sup θ ∈ Θ ∏ 1 n f ( x j | θ ) = L n ( θ n * ) L n ( θ ^ n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq1054.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
