Two sequential estimators are proposed for the odds p/(1-p) and log odds log(p/(1-p)) respectively, using independent Bernoulli random variables with parameter p as inputs. The estimators are unbiased, and guarantee that the variance of the estimation error divided by the true value of the odds, or the variance of the estimation error of the log odds, are less than a target value for any p in (0,1). The estimators are close to optimal in the sense of Wolfowitz's bound.
翻译:针对伯努利随机变量(参数为p)的胜率p/(1-p)和对数胜率log(p/(1-p)),分别提出了两种序贯估计方法。所提估计量具有无偏性,且对任意p∈(0,1),能保证胜率真实值下的估计误差方差与胜率真实值之比,或对数胜率估计误差方差,均小于设定的目标值。在沃尔福威茨界意义下,这些估计量接近最优。