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二乘二列联表的假设估计与可接受性剖面AI 解读

By estimating, rather than testing, hypotheses regarding the degree of dependence between the factors in 2 × 2 tables, the technical difficulties associated with small sample sizes are avoided. The estimators proposed here attempt to estimate 1 when the alternative hypothesis is true and 0 when the null hypothesis is true, subject to a bound on the squared error loss under the hypothesis. Such estimators provide guarded weights of evidence for the alternative hypothesis.…

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克拉美–拉奥型不等式的充要条件AI 解读

For a random variable $X$ with possible distributions indexed by a parameter $\theta$, and for real-valued $T = T(X)$ and $V = V(X, \theta)$ with $\operatorname{Var} T < \infty$ and $0 < \operatorname{Var} V < \infty$, Schwarz's inequality gives $\operatorname{Var} T \geqq \{\operatorname{Cov} (T, V)\}^2/\operatorname{Var} V$. Necessary and sufficient conditions are given for this inequality to be of Cramer-Rao type: $\operatorname{Var} T \geqq \{a_m(\theta)\}^2/\operatorname{Var} V$…

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