Statistical Inference and Hypothesis Testing-Cramer-Rao Inequality (ISS (Statistical Services) Statistics Paper II (New 2016 MCQ Pattern)): Questions 1 - 5 of 7

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Question number: 1

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

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MCQ▾

Question

Which of the following is not a regularity condition for Cramer-Rao Inequality?

Choices

Choice (4)Response

a.

The information function exists and is positive for all

b.

The derivative exists for all

c.

The parameter space , can have only positive values.

d.

The differentiation and integration of are interchangeable. In symbols

Question number: 2

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

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MCQ▾

Question

Regularity conditions of Cramer-Rao inequality are related to

Choices

Choice (4)Response

a.

Neither (i) and (ii)

b.

Differentiability of functions

c.

Integrability of functions

d.

Both b. and c. are correct

Question number: 3

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

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MCQ▾

Question

Which of the following options is appropriate for the Cramer-Rao Inequality, where

is an unbiased estimator -

Choices

Choice (4)Response

a.

b.

c.

d.

Question number: 4

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

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MCQ▾

Question

Cramer-Rao Inequality provides a ________ to the variance of an unbiased estimator for a parameter.

Choices

Choice (4)Response

a.

Upper bound

b.

Lower bound

c.

Upper bound and Lower bound

d.

None of the above

Question number: 5

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

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MCQ▾

Question

Cramer-Rao inequality with regard to the variance of an estimator provides

Choices

Choice (4)Response

a.

Lower bond on the variance

b.

Asymptotic variance of an estimator

c.

Upper bound on the variance

d.

All of the above

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