Difference between Factorization theorem and Fischer-Neymann theorem for t to be sufficient estimator of theta

cousinhaui

cousinhaui

Answered question

2022-10-30

Difference between Factorization theorem and Fischer-Neymann theorem for t to be sufficient estimator of θ

Answer & Explanation

DoryErrofbi

DoryErrofbi

Beginner2022-10-31Added 12 answers

The Fisher-Neymann factorization theorem says that if the density f can be factored into nonnegative functions g, h such that f ( x ) = h ( x ) g ( T ( x ) , θ ), then T ( x ) is a sufficient statistic for theta. Usually people say factorization theorem for short.
By contrast, the definition of sufficiency is that T ( x ) is a sufficient statistic for theta if f ( x | T ( x ) ) does not depend on theta.

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