Suppose that X1, . . . , Xn form a random sample from the normal distribution with

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Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean μ and unknown variance σ2. Let and be the two estimators of σ2, which are defined as follows:
Σx-Χ. . 6 ΣX,-X ) and 61 - i-1

Show that the M.S.E. of is smaller than the M.S.E. of for all possible values of μ and σ2.

Distribution
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Probability And Statistics

ISBN: 9780321500465

4th Edition

Authors: Morris H. DeGroot, Mark J. Schervish

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