FRM Part I · FRM Exam Part I · Sample Moments
Which statement about the sample variance estimator using n-1 in the denominator is correct, assuming i.i.d. observations?
The n-1 sample variance is an unbiased estimator of the population variance for i.i.d. data. Its square root, the sample standard deviation, remains slightly biased because the square root is nonlinear. The n-1 estimate is larger than the n-denominator estimate.
- AIt is an unbiased estimator of the population varianceCorrect
- BIts square root is an unbiased estimator of the population standard deviation
- CIt is always smaller than the estimator using n
- DIt equals the mean of the absolute deviations
Explanation
Dividing by n-1 corrects for using the sample mean in place of the true mean, making the variance estimator unbiased. The square root is a nonlinear transform, so the sample standard deviation is still biased (Jensen's inequality). The n-1 version is larger than the n version, not smaller.
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