ISS Statistics Paper II (New 2016 MCQ Pattern): Questions 243 - 244 of 246

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Question number: 243

» 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 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.

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.

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)

d.

All a. , b. and c. are correct

Question number: 244

» Statistical Inference and Hypothesis Testing » Cramer-Rao Inequality

MCQ▾

Question

Cramer-Rao Inequality provides a Lower bond to the variance of an ________ estimator for a parameter.

Choices

Choice (4) Response

a.

Unbiased

b.

Consistent

c.

Maximum Likelihood estimator

d.

Sufficient

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