Statistical Inference and Hypothesis Testing-Estimation Methods of Maximum Likelihood (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 15 - 19 of 35

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Question number: 15

» 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

Question number: 16

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

MCQ▾

Question

The MLE of the parameter α of the distribution 1Γ(λ)(λα)λeλxαxλ1;0x<,λ>0 is given by

Choices

Choice (4) Response

a.

MLE(α)=x¯

b.

MLE(α)=λx¯

c.

MLE(α)=2x¯

d.

MLE(α)=λx¯

Question number: 17

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

MCQ▾

Question

Consider a function θ^=(x1,x2,,xn) of the sample values. θ^ is said to be Maximum Likelihood Estimator (MLE) if

Choices

Choice (4) Response

a.

L(θ^)<L(θ)

b.

L(θ^)=L(θ)

c.

L(θ^)>L(θ)

d.

All of the above

Question number: 18

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

MCQ▾

Question

The maximum Likelihood Estimator of θ in f(x,θ)=(1+θ)xθ,0<x<1 is

Choices

Choice (4) Response

a.

Does not exists

b.

θ^=ni=1nlogxi1

c.

θ^=ni=1nlogxi1

d.

Question does not provide sufficient data or is vague

Question number: 19

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

MCQ▾

Question

The principle of Maximum Likelihood consists of finding an estimator, which ________ the likelihood function.

Choices

Choice (4) Response

a.

Minimizes

b.

Maximizes

c.

Maximizes or Minimizes

d.

All of the above

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