Statistical Inference and Hypothesis Testing-Cramer-Rao Inequality (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 1 - 3 of 7

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Question number: 1

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

MCQ▾

Question

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

Choices

Choice (4) Response

a.

The parameter space Θ , can have only positive values.

b.

The differentiation and integration of f(x;θ) are interchangeable. In symbols

dydθf(x;θ)dx=f(x;θ)θdx

c.

The information function I(θ)=E[θlogL]2 exists and 0<I(θ)< is positive for all θΘ

d.

The derivative θlogL(x;θ) exists for all θΘ

Question number: 2

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

MCQ▾

Question

Regularity conditions of Cramer-Rao inequality are related to

Choices

Choice (4) Response

a.

Integrability of functions

b.

Neither (i) and (ii)

c.

Differentiability of functions

d.

Both a. and c. are correct

Question number: 3

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

MCQ▾

Question

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

T is an unbiased estimator γ(θ) -

Choices

Choice (4) Response

a.

Var(T)[θlogL]2E[ddθγ(θ)]2

b.

Var(T)[ddθγ(θ)]2E[θlogL]

c.

Var(T)[ddθγ(θ)]2E[θlogL]2

d.

Var(T)[ddθγ(θ)]2E[θlogL]2

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