Statistical Inference and Hypothesis Testing-Minimum Variance Unbiased Estimators (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 4 - 7 of 15

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Question number: 4

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

Minimum Variance Unbiased Estimator (MVUE) is________

Choices

Choice (4) Response

a.

Not unique

b.

Unique

c.

Question does not provide sufficient data or is vague

d.

None of the above

Question number: 5

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

A statistic T=(x1,x1,,xn) is MVUE of γ(θ) if ………. where Tʹ is any other unbiased estimator of γ(θ)

Choices

Choice (4) Response

a.

Eθ(T)>γ(θ)andVARθ(T)=VARθ(Tʹ)forallθΘ

b.

Eθ(T)=γ(θ)andVARθ(T)VARθ(Tʹ)forallθΘ

c.

Eθ(T)=γ(θ)andVARθ(T)VARθ(Tʹ)forallθΘ

d.

Eθ(T)=γ(θ)andVARθ(T)VARθ(Tʹ)forallθΘ

Question number: 6

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

Uniformly minimum-variance unbiased estimator (UMVUE) or minimum-variance unbiased estimator (MVUE) is an unbiased estimator that has ________ than any other unbiased estimator for all possible values of the parameter.

Choices

Choice (4) Response

a.

Maximum variance

b.

Minimum variance

c.

zero variance

d.

None of the above

Question number: 7

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

Which of the following results are true for Minimum Variance Unbiased Estimator (MVUE) -

Choices

Choice (4) Response

a.

If T1a nd T2 are MVUE of γ1(θ) and γ2(θ) then α(T1)+β(T2) will be an MVUE of αγ1(θ)+βγ2(θ)

b.

The correlation coefficient between a most efficient estimator and any other estimator with efficiency e is e .

c.

MVUE is unique

d.

All a. , b. and c. are correct

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