Statistical Inference and Hypothesis Testing-Minimum Variance Unbiased Estimators (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 8 - 10 of 15

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Question number: 8

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

If T1 and T2 are two estimators for (θ) , such that E(T1)=E(T2)=γ(θ) and V(T1)=V(T2) , then

Choices

Choice (4) Response

a.

T1T2

b.

T1=T2

c.

Either T1>T2 or T2>T1

d.

Question does not provide sufficient data or is vague

Question number: 9

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

For a normal population N(μ,σ2) , both sample mean and sample median are unbiased and consistent estimators of μ . In this case, which one will be the efficient estimator?

Choices

Choice (4) Response

a.

Sample mean is more efficient estimator of μ than the sample median.

b.

Sample median is more efficient estimator of μ than the sample mean

c.

Sample mean and Sample median are equally efficient

d.

All of the above

Question number: 10

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

Suppose T1andT2 are the unbiased estimators of γ(θ) with Efficiencies e1 and e2 respectively. and ρ=ρθ is the correlation coefficient between them. Then

Choices

Choice (4) Response

a.

e1e2(1e1)(1e2)ρe1e2+(1e1)(1e2)

b.

e1e2(1+e1)(1+e2)ρe1e2+(1+e1)(1+e2)

c.

e1e2+(1e1)(1e2)ρe1e2(1e1)(1e2)

d.

e1(1e1)ρe2+(1e2)

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