Let X1, X2, . . . , Xn be a random sample from a pdf f(x) that
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Let X1, X2, . . . , Xn be a random sample from a pdf f(x) that is symmetric about m, so that is an unbiased estimator of
. If n is large, it can be shown that V( ) 1/(4n[ f(m)]2
).
a. Compare V( ) to V( ) when the underlying distribution is normal.
b. When the underlying pdf is Cauchy (see Example 6.7), V( ) , so is a terrible estimator. What is V( ) in this case when n is large?
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Related Book For
Probability And Statistics For Engineering And The Sciences
ISBN: 9781133169345
8th Edition
Authors: Jay L Devore, Roger Ellsbury
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