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Let X be a random variable with a distribution P_θ in {P_θ: θ ∈ Θ}, f_θ be the p.d.f. of P_θ w.r.t. a measure ν, A be an event, and PA = {f_θI_A/P_θ(A) : θ ∈ Θ}.

(a) Show that if T (X) is sufficient for P_θ ∈ P, then it is sufficient for P_θ ∈ P_A.

(b) Show that if T is sufficient and complete for P_θ ∈ P, then it is complete for P_θ ∈ P_A.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
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