Statistical Inference and Hypothesis Testing-Factorization Theorem (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 1 - 2 of 5

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Question number: 1

» Statistical Inference and Hypothesis Testing » Factorization Theorem

MCQ▾

Question

Equation is sufficient for Equation if and only if the joint density function Equation , of the sample values can be expressed in the form

Equation where Equation depends on Equation and Equation only through the value of Equation and Equation is independent of Equation . This Theorem is known as

Choices

Choice (4) Response

a.

Blackwell Theorem

b.

Rao-Blackwell Theorem

c.

Factorization Theorem

d.

Cramer-Rao Theorem

Question number: 2

» 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 Equation is said to be sufficient for Equation if it provides all the information contained in the sample about the parametric function Equation

b.

If Equation is a estimator of parameter Equation based on a sample Equation of size n from the population with density Equation such that the conditional distribution of Equation given T is independent of Equation then T is sufficient estimator of Equation .

c.

A statistic Equation is sufficient estimator of parameter Equation if and only if the likelihood function (joint p. d. f. of the sample) can be expressed as Equation where Equation is the p. d. f. of statistic Equation and Equation is a function of sample observations only independent of Equation

d.

All of the above

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