Resolving hypotheses with successive chisquares

摘要: A set of hypotheses H1,...Hk form a hierarchy if their respective parameter spaces are completely imbedded. That is, ω1 ⊃...⊃ωk, and the dimensions strictly ordered: D(ω1) >...>D(ωk). The most tenable hypothesis from given is selected by forming successive likelihood ratio chisquares Λ12,...Λ1k testing them in reverse order. first non-significant LR Chisquare, say, Λ1j, 2≤j≤k implies Hj should be as hierarchy.