Statistical Inference and Hypothesis Testing (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 139 - 140 of 222

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Question number: 139

» Statistical Inference and Hypothesis Testing » Factorization Theorem

MCQ▾

Question

Which of the following definitions of Sufficiency of a estimator is known as Fisher-Neyman Factorization Theorem?

Choices

Choice (4) Response
a.

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)

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.

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.

d. All of the above

Question number: 140

» Statistical Inference and Hypothesis Testing » Factorization Theorem

MCQ▾

Question

Factorization theorem for sufficiency is known as

Choices

Choice (4) Response
a.

Rao-Blackwell Theorem

b.

Fisher-Neyman Theorem

c.

Bernoulli Theorem

d.

Cramer-Rao Theorem

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