# Statistical Inference and Hypothesis Testing-Optimal Properties of Maximum Likelihood Estimators (ISS (Statistical Services) Statistics Paper II (New 2016 MCQ Pattern)): Questions 1 - 2 of 2

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## Question number: 1

» Statistical Inference and Hypothesis Testing » Optimal Properties of Maximum Likelihood Estimators

MCQ▾

### Question

Which of the following properties of MLE is not correct?

### Choices

Choice (4) Response

a.

If a sufficient statistic exists, it is a function of the Maximum Likelihood estimators.

b.

If a minimum variance bound (MVB) unbiased estimator exists, maximum likelihood estimator provides it.

c.

MLE is always unique

d.

When maximum likelihood estimators exists, it is most efficient for large samples under the assumptions that the distribution of the estimators tends to normal.

## Question number: 2

» Statistical Inference and Hypothesis Testing » Optimal Properties of Maximum Likelihood Estimators

MCQ▾

### Question

What properties of estimators are usually held by Maximum Likelihood estimators (MLE’s)?

### Choices

Choice (4) Response

a.

A MLE is not necessarily Unbiased

b.

A MLE may not be uniformly minimum variance unbiased estimator (UMVUE)

c.

A MLE is not necessarily unique

d.

All a. , b. and c. are correct

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