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点估计

点估计

点估计就是用单一的数值对总体的未知参数进行估计,我们用样本均值估计总体均值,用样本方差估计总体方差,用的就是点估计。如果一个估计量的抽样分布的均值与被估计的参数相等,我们称其为无偏的。而当一个估计量在样本容量趋于无穷时趋于被估计的参数,那我们便称其为一致的

Point estimation is to estimate the unknown statistics of the population by one single value. Using the mean or variation of the sample to estimate the mean or variation of the population, this belongs to the method of point estimation. If the mean of the distribution of the sample and the population is equal, this is an “unbiased” estimator. And if the estimator inclines to its real value when the sample size inclines to infinity, this is a “consistent” estimator.

此处需要注意,一致与无偏是两个概念,无偏估计指的是当样本的组数无限增加时,统计量趋于被估计量,而一致性指的是当样本容量无限增多时,统计量趋于被估计量。

It should be notices that unbiased and consistent are two different concepts. Unbiased estimation means that the statistics inclines to the estimator if the group amount inclines to infinity, but consistence means that the statistics inclines to the estimator if the sample size inclines to infinity.

点估计.txt · 最后更改: 2024/04/01 05:47 由 李佳熠2