Statistical Inference and Hypothesis Testing (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 54 - 57 of 222

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Question number: 54

» Statistical Inference and Hypothesis Testing » Minimum Variance Unbiased Estimators

MCQ▾

Question

An unbiased estimator T(x) of γ(θ) is the Minimum Variance Unbiased Estimator (MVUE) estimator if ________. Where Tʹ is any other unbiased estimator of γ(θ) .

Choices

Choice (4) Response

a.

VARθ(T(x))VARθ(Tʹ(x))forallθΘ

b.

VARθ(T(x))VARθ(Tʹ(x))forallθΘ

c.

VARθ(T(x))VARθ(Tʹ(x))forallθΘ

d.

VARθ(T(x))=1VARθ(Tʹ(x))forallθΘ

Question number: 55

» Statistical Inference and Hypothesis Testing » Estimation Methods of Maximum Likelihood

MCQ▾

Question

Maximum Likelihood Estimator (MLE) is the same regardless of whether we maximize the likelihood or the log-likelihood function. This statement is

Choices

Choice (4) Response

a.

False

b.

True

c.

True only if L < 0

d.

Question does not provide sufficient data or is vague

Question number: 56

» Statistical Inference and Hypothesis Testing » Estimation Methods of Maximum Likelihood

MCQ▾

Question

MLE’s are always consistent estimators. This Theorem is known as

Choices

Choice (4) Response

a.

Rao-Blackwell Theorem

b.

Baye’s Theorem

c.

Hazoor Bazar’s Theorem

d.

Cramer-Rao Theorem

Question number: 57

» Statistical Inference and Hypothesis Testing » Estimation Methods of Maximum Likelihood

MCQ▾

Question

If MLE exists, it is the most efficient in the class of such estimators.

Choices

Choice (4) Response

a.

True only for some distributions

b.

False

c.

True

d.

None of the above

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