Statistical Inference and Hypothesis Testing-Estimation Methods of Maximum Likelihood (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 1 - 5 of 35

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Question number: 1

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

MCQ▾

Question

If T is the MLE of θ and ψ(θ) is one to one function of θ , then ψ(T) is the MLE of ψ(θ) . This is known as the

Choices

Choice (4) Response

a.

Asymptotic Normality of MLE

b.

Consistency property of MLE

c.

Invariance property of MLE

d.

None of the above

Question number: 2

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

MCQ▾

Question

In a random sampling from Normal population N(μ,σ2), the likelihood estimators of mean and variance are

Choices

Choice (4) Response

a.

Variance is Unbiased

b.

Mean is biased

c.

Both a. and b. are correct

d.

Question does not provide sufficient data or is vague

Question number: 3

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

MCQ▾

Question

MLE’s are always consistent and unbiased estimators. This statement is

Choices

Choice (4) Response

a.

False

b.

True

c.

Always Unbiased estimators

d.

Question does not provide sufficient data or is vague

Question number: 4

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

MCQ▾

Question

In a random sampling from Normal population N(μ,σ2) the Maximum Likelihood estimator for σ2 is

Choices

Choice (4) Response

a.

σ^2=1ni=1n(xiμ)2

b.

σ^2=1n2i=1n(xiμ)2

c.

σ^2=i=1n(xiμ)2

d.

σ^2=1n1i=1n(xiμ)2

Question number: 5

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

MCQ▾

Question

The estimate of the MLE(α) of a population having density function

2α2(αx),0<α<x is

Choices

Choice (4) Response

a.

Not an Unbiased estimate of α

b.

Unbiased estimate of α2

c.

Unbiased estimate of α

d.

Question does not provide sufficient data or is vague

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