论文标题
广义估计器，坡度，效率和Fisher信息界限
Generalized Estimators, Slope, Efficiency, and Fisher Information Bounds
论文作者
论文摘要
点估计器可能不存在，不必是唯一的，并且它们的分布也不是参数不变的。广义估计器提供的分布是参数不变的，独特的，并且在估计值不存在时存在。当估计器偏差时，使用方差比较点估计器的用处较小。定义了一个平方坡$λ$，可用于比较点和广义估计器，并且不受偏置的影响。 Fisher Information $ i $和差异从根本上是不同的数量：后者是在不需要属于家庭的分布中定义的，而没有分配的家族（$ M $）不能定义前者。 Fisher Information和$λ$的数量相似，因为两者都在切线捆绑包$ t \！m $和$ i $上定义了上限，$λ\ le i $，对于所有样本尺寸 - 不需要 - 渐近学。使用$λ$而不是差异比较估计器支持Fisher的说法，即$ i $即使在小样本中也提供了限制。定义了$λ$ - 效率，该效率扩大了基于方差的无偏估计器的效率。虽然由坡度定义，但$λ$效率仅为$ρ^{2} $，这是估算器和得分函数之间相关性的平方。
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 $Λ$ 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 $Λ$ are similar quantities as both are defined on the tangent bundle $T\!M$ and $I$ provides an upper bound, $Λ\le I$, that holds for all sample sizes -- asymptotics are not required. Comparing estimators using $Λ$ rather than variance supports Fisher's claim that $I$ provides a bound even in small samples. $Λ$-efficiency is defined that extends the efficiency of unbiased estimators based on variance. While defined by the slope, $Λ$-efficiency is simply $ρ^{2}$, the square of the correlation between estimator and score function.
