题目
Otema Chi has a spreadsheet with 108 monthly returns for shares in Marunou Corporation. He writes a software program that uses bootstrap resampling to create 200 resamples of this Marunou data by sampling with replacement. Each resample has 108 data points. Chi’s program calculates the mean of each of the 200 resamples, and then it calculates that the mean of these 200 resample means is 0.0261. The program subtracts 0.0261 from each of the 200 resample means, squares each of these 200 differences, and adds the squared differences together. The result is 0.835. The program then calculates an estimate of the standard error of the sample mean. The estimated standard error of the sample mean is closest to:
选项
A.0.0115
B.0.0648
C.0.0883
答案
B
解析
B is correct.The estimate of the standard error of the sample mean with bootstrap resampling is calculated as follows:「huixue_img/importSubject/1564548696060858368.png」 B是正确的。 在bootstrapping中，它的步骤是这样的：1.从总体中随机抽取n个数作为样本，把这个样本集（sample）视为“（新）总体”；2.从（新）总体中，抽取第一个样本后放回，再抽取第二个再放回，以此类推，重复n次；重复抽样形成第一个样本集1（样本容量和新总体相同，均为n）3.不断重复第二步，形成B个样本集（样本1，样本2……样本B）；4.计算每一个样本集的均值X拔（共B个），并计算所有B个样本均值的均值E(X拔)。5.计算B个样本均值的标准差，即估计量的标准误，公式如下图。 从上述过程看出：从总体中抽取得到的sample 当做一个新的总体，那么sample mean就是样本，对样本求标准差，带入的是样本方差的计算公式然后开根号即可，计算出的就是题目要求解的答案。故，此时样本平均值的标准误差估计值，带入公式计算如下图：