Exercise Solution 4.3
- We first prove the technical result. This involves no random quantities. It is just algebra:
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- We next use our technical result to determine the bias of the sample variance estimator
[4.5]
The derivation is
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To obtain the next step in the derivation, we apply the result of Exercise 3.15 twice:
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We conclude that sample estimator [4.5] is biased.
- Finally, we determine the bias of the alternative estimator of variance
[4.27]
which we can denote
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The derivation largely parallels that of part (b):
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Estimator [4.27] is unbiased.