Suppose that X1,...,Xn form a random sample from

Chapter 7, Problem 8

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QUESTION:

Suppose that X1,...,Xn form a random sample from an exponential distribution for which the value of the parameter is unknown ( > 0). Is the M.L.E. of a minimal sufficient statistic?

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QUESTION:

Suppose that X1,...,Xn form a random sample from an exponential distribution for which the value of the parameter is unknown ( > 0). Is the M.L.E. of a minimal sufficient statistic?

ANSWER:

Step 1 of 4

If statistic  is a sufficient statistic for parameter , then the maximum likelihood estimator  depends on  only through , and if the is sufficient, then it is minimal sufficient statistic.

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