Suppose that T(X)T(X) is sufficient for , and that (X)(X) and (T(X))(T(X)) are the LRT statistics based on XX and T(X)T(X) respectively If a size LRT rejects H0H0 when (T(X))0 261(T(X))0 261, is the LRT that rejects H0H0 when (X)(X) also a size test ...

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Suppose that T(X)T(X) is sufficient for , and that (X)(X) and (T(X))(T(X)) are the LRT statistics based

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Suppose that T(X)T(X) is sufficient for θθ, and that λ(X)λ(X) and λ∗(T(X))λ∗(T(X)) are the LRT statistics based on XX and T(X)T(X) respectively. If a size-αα LRT rejects H0H0 when λ∗(T(X))≤0.261λ∗(T(X))≤0.261, is the LRT that rejects H0H0 when λ(X)λ(X) also a size-αα test?