Statistical Inference and Hypothesis Testing-Factorization Theorem (ISS (Statistical Services) 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

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

where depends on and only through the value of and is independent of . 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 is said to be sufficient for if it provides all the information contained in the sample about the parametric function

b.

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

c.

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

d.

All of the above

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