Estimation (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 9 - 13 of 14
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Question number: 9
» Estimation » Optimal Properties » Sufficient Estimator
Appeared in Year: 2015
Describe in Detail
Obtain the sufficient statistics for the following distribution.
(i)
(ii)
Explanation
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Question number: 10
» Estimation » Estimation Methods » Methods of Moments
Appeared in Year: 2015
Describe in Detail
The observations
3.9, 2.4, 1.8, 3.5, 2.4, 2.7, 2.5, 2.1, 3.0, 3.6, 3.6, 1.8, 2.0, 4.0, 1.5
are a random sample from a rectangular population with pdf
Estimate the parameters by the method of moments.
Explanation
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Question number: 11
» Estimation » Optimal Properties » Cramer-Raoinequality
Appeared in Year: 2015
Describe in Detail
Stating the regularity conditions, give the Cramer-Rao lower bound for the variance of an unbiased estimator of a parameter. Give an example, each, of a situation where the regularity conditions (i) does not hold (ii) holds
Explanation
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Question number: 12
» Estimation » Optimal Properties » Rao-Blackwell Theorem
Appeared in Year: 2015
Describe in Detail
Explain how the Rao-Blackwell theorem helps one to find a uniformly minimum variance unbiased estimator (UMVUE) of an unknown parameter. What is the relevance of the Lehman-Scheffe theorem in this scenario? If X 1, X 2, …, X n are Bin (1, p) variates, find the UMVUE of p.
Explanation
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Question number: 13
» Estimation » Optimal Properties » Minimum Variance Bound Estimators
Appeared in Year: 2015
Describe in Detail
Let X 1, X 2, …, X n be a random sample from the probability distribution with density
= 0; otherwise
where 0 < θ < ∞. Show that is a minimum variance bound estimator and has variance .
Explanation
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