Point estimators may not exist, need not be unique, and their distributions are not parameter invariant. Generalized estimators provide distributions that are parameter invariant, unique, and exist when point estimates do not. Comparing point estimators using variance is less useful when estimators are biased. A squared slope $\Lambda$ is defined that can be used to compare both point and generalized estimators and is unaffected by bias. Fisher information $I$ and variance are fundamentally different quantities: the latter is defined at a distribution that need not belong to a family, while the former cannot be defined without a family of distributions, $M$. Fisher information and $\Lambda$ are similar quantities as both are defined on the tangent bundle $T\!M$ and $I$ provides an upper bound, $\Lambda\le I$, that holds for all sample sizes -- asymptotics are not required. Comparing estimators using $\Lambda$ rather than variance supports Fisher's claim that $I$ provides a bound even in small samples. $\Lambda$-efficiency is defined that extends the efficiency of unbiased estimators based on variance. While defined by the slope, $\Lambda$-efficiency is simply $\rho^{2}$, the square of the correlation between estimator and score function.
翻译:点估计值可能不存在, 也不一定是独特的, 并且其分布量根本不同 。 一般估计值提供分布值, 参数不易变, 独特, 且在点估计不时存在。 使用差异比较点估计值在估计值有偏差时用处不大。 平方斜度 $\Lambda$ 定义可以用来比较点和通用估计值, 不受偏差的影响 。 Fisher 信息 $I 和 差异数量基本不同 : 后者定义的分布值不需要属于一个家庭, 而前者定义的分布值是不需要属于一个家庭的, 而前者定义的分布值是非分布式的, $M$。 Fishereral 和 $\\ Lambda$是相似的数量, 两者的定义都是相近的 $T\! m$ 和 $I 提供上限, $Lbda\ 美元, 所有的样本都持有 -- immptotictretime 。 使用美元而不是差异 支持 Fisheral $- dal developlexnal developmental laxldal lax lax lax the slax lax lax the lax lax lax lax lax lax lax lax lax lax lax lax lab ladal lab ladal ladal ladal lax ladal le ladal ladal ladal ladal le lad lex lex lex exb lex extrax lex lex lab lax lax lab extrax lex lex lex lex lex exal le le le le lab lab explab lab le le le lab lab le lab lab exb le le le le le le exal exal lab lab 美元 美元 美元 美元。