Likelihood ratio tests for comparing k populations - the two-parameter nonregular models (Q1085539)

Let \(\Omega =\{(\theta_ 1,\theta_ 2):c<\theta_ 1<\theta_ 2<d\}\) where (c,d) is a given (finite or infinite) interval, and let \(f(x,\theta_ 1,\theta_ 2)\), \((\theta_ 1,\theta_ 2)\in \Omega\), be a two truncation parameter density defined by \(f(x,\theta_ 1,\theta_ 2)=h(x)/g(\theta_ 1,\theta_ 2)\), \(\theta_ 1\leq x\leq \theta_ 2\). The authors study the likelihood ratio statistics for testing the homogeneity of k parameterized populations having densities \(f(x,\theta^ i_ 1,\theta^ i_ 2)\), \(i=1,2,...,k\), and obtain the limiting null as well as non-null distributions of the test statistics.