4. (a) Show that T and T2 are equivalent statistics if, and only if, we can write T, = H(T1) for some 1-1 transformation H of the range of T into the range of T2. Which of the following statistics are equivalent? (Prove or disprove.)

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4. (a) Show that T1 and T2 are equivalent statistics if, and only if, we can write T2 = H(T1)
for some 1-1 transformation H of the range of T into the range of T2. Which of the
following statistics are equivalent? (Prove or disprove.)
(b) II, *, and log x,, c; >0
(c) -1 Ti and E-, log ri, x; > 0
(d) (Σ" σ,, ΣΕ ο?) and (Σ o ΣL (οι- 3)?)
(e) (E, Ti, E-1 ) and (E ri, E (*; – 1)*).
Xi,
Transcribed Image Text:4. (a) Show that T1 and T2 are equivalent statistics if, and only if, we can write T2 = H(T1) for some 1-1 transformation H of the range of T into the range of T2. Which of the following statistics are equivalent? (Prove or disprove.) (b) II, *, and log x,, c; >0 (c) -1 Ti and E-, log ri, x; > 0 (d) (Σ" σ,, ΣΕ ο?) and (Σ o ΣL (οι- 3)?) (e) (E, Ti, E-1 ) and (E ri, E (*; – 1)*). Xi,
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