Estimation-Optimal Properties (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 6 of 8

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Question number: 1

» Estimation » Optimal Properties » Complete Statistics

Appeared in Year: 2014

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Define completeness. Verify whether Bin (1, p) is complete.

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Question number: 2

» Estimation » Optimal Properties » Sufficient Estimator

Appeared in Year: 2014

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Show that is not a sufficient estimator of the Bernoulli parameter θ.

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Question number: 3

» Estimation » Optimal Properties » Confidence Interval Estimation

Appeared in Year: 2015

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Let y 1, y 2, …, y n be a random sample from N (µ, σ 2) where µ and σ 2 are both unknown. Obtain a confidence interval of µ with confidence coefficient (1-α)

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Question number: 4

» Estimation » Optimal Properties » Sufficient Estimator

Appeared in Year: 2015

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Obtain the sufficient statistics for the following distribution.

(i)

(ii)

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Question number: 5

» 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

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Question number: 6

» 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.

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