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notinhk · 2022年01月18日

题目让计算标准误,而答案给的是样本标准差吧?

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:


我理解样本标准差s的计算按照定义应该是0.835除以199,然后开根号,得到s=0.0648 而题目问的是标准误,应该用s再除以根号下108 请老师详细解释下这道题,谢谢!
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星星_品职助教 · 2022年01月18日

同学你好,

这道题基础班上课已经讲过。

本题计算方式即为bootstrap下标准误的计算公式,代入即可。和中心极限定理下的标准误计算方式无关。

即使在中心极限定理下考察标准误,大概率也不会要求先行计算样本标准差,而是直接给出sx的值。直接计算sx/根号n。

bootstrap下标准误公式详见截图一。

基础班上对应这道题的讲解见截图二。

星星_品职助教 · 2022年01月23日

@王秋宇

不同的背景用不同的公式。

题干中明显表明了bootstraping的背景:“... that uses bootstrap resampling....”,直接代入对应公式即可。

“除以根号n”的公式和这道题没有任何关系,一般的应用场景是计算检验统计量的置信区间或对其做假设检验。

王秋宇 · 2022年01月23日

您好助教老师,我和这位同学有同样的疑惑。您的回答我看了,老师的讲解我也看了。您解释的是从公式角度。但是您能不能从原理角度讲解一下,为什么不能再除以根号N,也就是根号108。如何判断就一定要用bootstrap公式。 这题虽然没给方差,但是给了方差之和,方差之和除以199,再除以108,然后开根号。 这里面的区别是不是出在抽样方法上?

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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

2024-04-29 10:49 1 · 回答

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.0.0115B.0.0648C.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 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

2023-12-26 23:31 1 · 回答

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.0.0115B.0.0648C.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 这里的 108 points ta 怎么理解

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2022-05-21 15:50 1 · 回答

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