Statistical Inference and Hypothesis Testing-Sufficient Estimator (ISS Statistics Paper II (New 2016 MCQ Pattern)): Questions 1 - 4 of 8

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Question number: 1

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

Let x1,x2,.,xn be a random sample from a density function f(x,θ) . A statistics

T=t(x1,x2,.,xn) is said to be sufficient statistics if the conditional distribution of x1,x2,.,xn given T

Choices

Choice (4) Response
a.

Independent of θ S

b.

Dependent of T

c.

Dependent of θ

d.

Independent of T

Question number: 2

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

If a statistics T=t(X1,X2,.,Xn) is a sufficient statistics for a parameter θ of the density function (x;θ) , then the conditional distribution of X1,X2,.,Xn is ………. of θ for any value of T=t

Choices

Choice (4) Response
a.

Dependent

b.

Either dependent or Independent

c.

Independent

d. All of the above

Question number: 3

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

A statistic T=t(x1,x2,..,xn) is called as ________ Estimator for the parameter θ, if the conditional distribution of x1,x2,..,xn given T does not depend on θ.

Choices

Choice (4) Response
a.

Unbiased

b.

Maximum Likelihood estimator

c.

Efficient

d.

Sufficient

Question number: 4

» Statistical Inference and Hypothesis Testing » Sufficient Estimator

MCQ▾

Question

Let x1,x2,..,xn be a random sample from a uniform population on [0,θ] . Then the sufficient estimator for θ is

Choices

Choice (4) Response
a.

θ^=Minxi

b.

Either (i) or (ii)

c.

θ^=Maxxi

d. Question does not provide sufficient data or is vague

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