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 Equation be a random sample from Equation . Then the sufficient estimator for Equation is

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

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 Equation provides as much information as the random variable Equation 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 Equation is said to be sufficient for a parameter Equation , 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 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

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.

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

d.

All a. , b. and c. are correct

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