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

Essay Question▾

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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

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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

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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

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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

Essay Question▾

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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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