On Statistics Independent of a Complete Sufficient Statistic

摘要: If {Ρ θ}, θЄΩ, be a family of probability measures on an abstract sample space \(\mathcal {G}\) and Τ sufficient statistic for θ then T 1 to stochastically independent it is necessary that the distribution θ. The condition also if boundedly complete statistic. Certain well-known results theory follow immediately from above considerations. For instance, x 1, 2,. . , n are Ν(μ, σ)’s mean \(\bar x\) variance s 2 mutually jointly any f (real or vector valued) change scale origin. It deduced 2, ., random variables such their joint involves unknown location parameter there can exist linear only x’s all normal. Similar characterizations Gamma indicated.