分组数据参数的单边估计与检验
One-sided Estimating and Testing Problems from Grouped Samples
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摘要: 设x0＜ｘ1＜…＜xk-1＜xk是分布函数Ｆ（ｘ－θ）支撑集上的分点．令ｎｉ表示落入区间（xi-1，xi）的观测值个数，并称其为分组数据．本文讨论了θ在θ≥θ0下的最大似然估计存在且唯一的条件及其渐近性质；给出了利用分组数据求最大似然估计的方法．最后；讨论了θ的单边检验问题。Abstract: Let x0＜ｘ1＜…＜xk-1＜xk be dividing points of a support set of the distribution function F（x-θ）, by ni denote the number of observations falling in the interval (xi-1, xi and said ni’s to be grouped samples.
In this paper, we give some conditions of existence and uniqueness of the MLE of θ for grouped samples under a restriction θ≥θ0 with some given θ0 The one-sided testing problem under the restriction is also considered in this paper.
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