Statistical Inference and Hypothesis Testing-Sufficient Estimator (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 5 - 8 of 8

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Question number: 5

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

Let x1,x2,..,xn be a random sample from N(μ,σ2)population . Then the sufficient estimator for μ is

Choices

Choice (4) Response

a.

ni=1nxi

b.

1ni=1nxi

c.

i=1nxi

d.

Question does not provide sufficient data or is vague

Question number: 6

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

If a statistic T=t(x1,x2,..,xn) provides as much information as the random variable T=x1,x2,..,xn could provide, Then T is a ________ Statistic

Choices

Choice (4) Response

a.

Efficient

b.

Unbiased

c.

Sufficient

d.

Consistent

Question number: 7

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

An estimator T=t(x1,x2,..,xn) is said to be sufficient for a parameter θ , if it

Choices

Choice (4) Response

a.

If it converges to the parameter in probability

b.

Contains all the information in the sample regarding the parameter.

c.

Contains no information in the sample regarding the parameter

d.

Question does not provide sufficient data or is vague

Question number: 8

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

Which of the definition is true for Sufficiency of an estimator?

Choices

Choice (4) Response

a.

A statistic T=t(x1,x2,.,xn) is sufficient estimator of parameter θ if and only if the likelihood function (joint p. d. f. of the sample) can be expressed as L=i=1nf(xi,θ)=g(t,θ).k(x1,x2,.,xn) where g(t,θ) is the p. d. f. of statistic t and k(x1,x2,.,xn) is a function of sample observations only independent of θ.

b.

If T=t(x1,x2,.,xn) is a estimator of parameter θ, based on a sample x1,x2,.,xn of size n from the population with density f(x,θ) such that the conditional distribution of x1,x2,.,xn given T is independent of θ, then T is sufficient estimator of θ .

c.

An estimator Tn is said to be sufficient for τ(θ) if it provides all the information contained in the sample about the parametric function τ(θ)

d.

All a. , b. and c. are correct

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