Statistical Inference and Hypothesis TestingFactorization 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
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.  RaoBlackwell Theorem 

c.  Factorization Theorem 

d.  CramerRao Theorem 

Question number: 2
» Statistical Inference and Hypothesis Testing » Factorization Theorem
Question
Which of the following definitions of Sufficiency of a estimator is known as FisherNeyman 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 
