MOM Estimator for Normal Parameters
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Setup:
. - Goal: Find MOM estimates for
.
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Step 1: First Moment:
- Theoretical:
. - Sample:
. - Estimator:
.
- Theoretical:
-
Step 2: Second Moment:
- Theoretical:
. - Sample:
. - Equate:
.
- Theoretical:
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Derivation:
- Substitute
: .
- Rewrite as summation:
.
- Substitute
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Bias Property:
- The MOM estimator for variance is biased.
. - It divides by
, whereas the unbiased sample variance ( ) divides by .
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Footnotes