Herschel on Estimation
本文回顾了赫歇尔对统计估计问题的长期兴趣,包括他给出的概率分布证明、引入双变量可能误差,以及从圆形区域内观测比例估计参数的方法,并验证了他对估计值随同心圆半径增大而增加的解释。
Sir John Herschel expressed an interest from time to time over a long period in a problem that would now be called statistical. He gave his own proof of a relevant probability distribution, introduced a bivariate version of the probable error and estimated this parameter from the proportion of observations within a circular area. When theory was applied to observation, he noticed that estimates obtained from different concentric circles steadily increased with distance from the centre. Herschel suggested an explanation which is confirmed here.