Question

proof the theorem 1

rst of Robert V. Hogg, Allen Craig-lntroduction t no say e instances it ma ul roblem ean be avoided if we will but prove the following factorization theorem of Neyman. Theorem 1. Let a distribution that has pdf. f(x, θ), θ62. The statistic Y1= n(x, , x2, . . . , X") is a suficient statistic for θ if and only if we can find two nonnegative functions, kj and k2, such that t X,, X2,..., X, denote a random sample fronm - ki[ui(x,i, x2, . . . , x); S^kz(xi, x2, .. ., x.), where k2(x1, x2, . . . , x.) does not depend upon θ.

Answer 1

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