Provide an estimator of
Prove that the estimator is consistent.
Explain whether the estimator is a
Also provide the implication.
Answer to Problem 69E
The method of moments estimator of
Explanation of Solution
Calculation:
The expectation of the given random variable Y is obtained as follows:
Consider that the method of moments estimator of
Now, to obtained the method of moments estimator of
Hence, the method of moments estimator of
Now consider,
Thus,
Now,
The variance of Y is given as follows:
The variance of
Thus, the estimator
Now, using Law of large numbers it can be aid that
That is,
Hence,
The likelihood function of α can be written as follows:
Where
By Theorem 9.4 (Factorization theorem), it can be said that,
Hence, the estimator is estimator is not a function of the sufficient statistic
Therefore, it implies that it is not a minimum variance unbiased estimator.
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Chapter 9 Solutions
Mathematical Statistics with Applications
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill