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。。 · 2025年07月07日

关于样本方差和总体方差

  1. FRM I
  2. Quantitative

NO.PZ2023091601000018

问题如下：

The CIO of a global macro fund is assessing the performance of theinternational portfolio managers of the fund. The CIO gathers the annualizedtotal returns of a sample of the managers as presented in the following table:

The CIO calculatesthe central moments of these returns. What is the correct unbiased samplevariance of the returns data?

选项：

A.

0.00128

B.

0.00160

C.

0.00288

D.

0.00360

解释：

B is correct. Theunbiased estimator for the sample variance is given by:


From the values inthe table, μ is obtained as (21%+17%+11%+18%+13%)/5 = 16%. Therefore,

S2=[(21% − 16%)2 + (17% − 16%)2 + (11% − 16%)2 +(18% − 16%)2 + (13% − 16%)2]/(5-1)=0.00160

A is incorrect.This is a biased estimate as it divides by n=5 and not by n-1=4

C is incorrect.This uses a μ that is adjusted with n-1, resulting in 20%, while also dividingthe numerator of the sample estimator by 5 and not 4.

D is incorrect.This uses a μ that is adjusted with n-1, resulting in 20%.

可不可以认为无偏估计量的方差就是总体方差，而这种将所有结果列举出来的就是一个总体，直接计算总体方差

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1 个答案

李坏_品职助教 · 2025年07月07日

嗨，努力学习的PZer你好：


这道题问的是样本方差（sample variance）的无偏估计结果是什么。 他给了你一个样本的列表，让你计算这个样本方差的无偏估计结果。 答案里的 S^2就是样本方差的无偏估计。


而总体方差指的是某个序列全部所有的数据包含在内，计算出来的方差。但大部分情况下我们是不可能拿到全部数据的，所以算不出来总体方差。 只能先去抽样，得到一个样本，然后用样本方差来代替总体方差。

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NO.PZ2023091601000018 问题如下 The CIO of a globmacro funis assessing the performanof theinternationportfolio managers of the fun The CIO gathers the annualizeotreturns of a sample of the managers presentein the following table:The CIO calculatesthe centrmoments of these returns. Whis the correunbiasesamplevarianof the returns t A.0.00128 B.0.00160 C.0.00288 0.00360 B is correct. Theunbiaseestimator for the sample varianis given by: From the values inthe table, μ is obtaine(21%+17%+11%+18%+13%)/5 = 16%. Therefore,S2=[(21% − 16%)2 + (17% − 16%)2 + (11% − 16%)2 +(18% − 16%)2 + (13% − 16%)2]/(5-1)=0.00160A is incorrect.This is a biaseestimate it vis n=5 annot n-1=4C is incorrect.This uses a μ this austewith n-1, resulting in 20%, while also vingthe numerator of the sample estimator 5 annot 4.is incorrect.This uses a μ this austewith n-1, resulting in 20%.

2025-03-01 16:54 1 · 回答