Statistical Inference and Hypothesis Testing-Minimum Variance Unbiased Estimators (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 11 - 14 of 15

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Question number: 11

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

If T1 and T2 are two unbiased estimators of γ(θ) based on the random sample X1,X2,Xn , then T1 is said to be UMVUE if and only if

Choices

Choice (4) Response
a.

V(T1)=V(T2)

b.

V(T1)>V(T2)

c.

V(T1)<V(T2)

d.

V(T1)V(T2)

Question number: 12

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

If T1 is an MVU estimator of γ(θ) for all θΘ and T2 is any other unbiased estimator of γ(θ) with efficiency e=eθ , then the correlation coefficient between T1andT2 is given by

ρ=e all θΘ

Choices

Choice (4) Response
a.

ρ=12e for all θΘ

b.

ρ=e2 for all θΘ

c.

ρ= 1e for all θΘ

d.

ρ=e for all θΘ

Question number: 13

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

A Minimum Variance Unbiased Estimator T1 is said to be unique if for any other estimator T2 ,

Choices

Choice (4) Response
a.

VAR(T1)VAR(T2)

b.

VAR(T1)VAR(T2)

c.

Neither (i) nor (ii)

d. Question does not provide sufficient data or is vague

Question number: 14

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

If T1 and T2 are two Minimum Variance Unbiased (MVU) estimators for γ(θ), then

Choices

Choice (4) Response
a.

Either T1>T2 or T2>T1

b.

T1T2

c.

T1=T2

d. Question does not provide sufficient data or is vague

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