基于符号检验对分位数最短区间估计的探讨

Study on the shortest interval estimation of quantile based on sign test

从符号检验出发,在理论上推导出分位点在样本容量和显著性水平一定时的最短区间估计模型,并与一般分位点区间估计形式做比较。发现中位数的常用区间估计形式与最短区间估计重合,且与样本容量无关;而在其他分位点考虑最短区间估计具有一定意义。利用趋势检验说明,随着分位点趋于0.5,一般区间估计形式与最短区间估计的不一致性在减弱。

Based on the sign test,the shortest interval estimation of a quantile is theoretically derived and compared with the general form of quantile interval estimation with a given sample size and significance level.It is found that the common interval estimation forms of the median coincide with the shortest interval estimation and is independent of sample size;It is significant to consider the shortest interval estimation in other quantiles.The trend test shows that the inconsistency between the general interval estimation and the shortest interval estimation decreases as the quantile approaches 0.5.