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James · 2023年12月26日

总体也就是108个月的收益，每个样本都抽了108个收益，然后重复抽样了200次

  1. CFA I
  2. Quantitative

NO.PZ2021062201000014

问题如下：

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

解释：

B is correct.

The estimate of the standard error of the sample mean with bootstrap resampling is calculated as follows:


使用 bootstrap resampling对样本均值的标准误的估算如下：


如题，这道题感觉每一次重复抽样都把总体抽完了呀，也就是说每一次抽样抽出来的东西都是一样的，那重复抽200次也没有意义了呀

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1 个答案

品职助教_七七 · 2023年12月27日

嗨，努力学习的PZer你好：


bootstrap是有放回的抽样，第1个抽出来后再放回，将来就还有可能再被抽出来一次。同理，每一个样本抽出来再放回后，都有可能在后续被再次抽出来。

假设原始的sample是1,2,3,4......107,108，bootstrap resample中的108个样本点的构成就有可能是1,1,1,2,3,4,4，...,107,107；或者1,2,2,2,3,3,3，....105,108这种；不会是“每一次抽样抽出来的东西都是一样的”。

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NO.PZ2021062201000014 问题如下 Otema Chi ha spreaheet with 108 monthly returns for shares in Marunou Corporation. He writes a software progrthuses bootstrresampling to create 200 resamples of this Marunou ta sampling with replacement. Earesample h108 ta points. Chi's progrcalculates the meof eaof the 200 resamples, anthen it calculates ththe meof these 200 resample means is 0.0261. The progrsubtracts 0.0261 from eaof the 200 resample means, squares eaof these 200 fferences, anas the squarefferences together. The result is 0.835. The progrthen calculates estimate of the stanrerror of the sample mean.The estimatestanrerror of the sample meis closest to: A.0.0115 B.0.0648 C.0.0883 B is correct.The estimate of the stanrerror of the sample mewith bootstrresampling is calculatefollows: 使用 bootstrresampling对样本均值的标准误的估算如下 Otema Chi ha spreaheet with 108 monthly returns for shares in Marunou Corporation. He writes a software progrthuses bootstrresampling to create 200 resamples of this Marunou ta sampling with replacement. Earesample h108 ta points. Chi's progrcalculates the meof eaof the 200 resamples, anthen it calculates ththe meof these 200 resample means is 0.0261. The progrsubtracts 0.0261 from eaof the 200 resample means, squares eaof these 200 fferences, anas the squarefferences together. The result is 0.835. The progrthen calculates estimate of the stanrerror of the sample mean. Earesample h108 ta points. 请问这个B不应该是108吗？为什么是200

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