Chapter 6: Point Estimation

Question 1

Point Estimate

Answer 1

Question 2

Point Estimator

Answer 2

Question 3

General Concepts of Point Estimation

Answer 3

Question 4

General Concepts of Point Estimation (contd.)

Answer 4

Question 5

Example 2

Answer 5

Question 6

Example 2 contd.

Answer 6

Question 7

Accurate Estimator

Answer 7

• for some samples, the estimator will yield a larger value while others will underestimate

Question 8

Expected or mean squared error

Answer 8

Question 9

Unbiasedness

Answer 9

Question 10

Unbiased Estimators

Answer 10

Question 11

Unbiased Estimators (contd.)

Answer 11

• Suppose (theta) is an unbiased estimator;
• then if theta= 100, the (theta-hat) sampling distribution is centered at 100;
• if theta = 27.5, then the (theta-hat) sampling distribution is centered at 27.5, and so on.

Question 12

Recognizing unbiasedness without knowing parameter

Answer 12

Question 13

Unbiasedness Equation Theorem

Answer 13

Question 14

Principle of Unbiased Estimation

Answer 14

Question 15

Calculating Unbiased Estimator

Answer 15

Question 16

Answer 16

Question 17

Estimators with Minimum Variance

Answer 17

Question 18

Estimators with Minimum Variance (contd.)

Answer 18

Question 19

Example 7

Answer 19

Question 20

Example 7 Solution

Answer 20

Question 21

Example 7 Solution (contd.)

Answer 21

Question 22

Reporting a Point Estimate: The Standard Error

Answer 22

Question 23

Example 9

Example 2 continued…

Question 24

More on The Standard Error

Answer 24

Question 25

Point Estimation - to summarize

Answer 25

Question 26

Point Estimation - to summarize (contd.)

Answer 26

Question 27

Formulating Estimators

Answer 27

Question 28

The Method of Moments (MoM)

The basic idea of MoM :

• Equate certain sample characteristics, such as the mean, to the corresponding population expected values.
• Then solving these equations for unknown parameter values yields the estimators.

Answer 28

Question 29

The Method of Moments (MoM) (contd.)

Answer 29

Question 30

Example 12

Question 31

Maximum Likelihood Estimation

Answer 31

The method of maximum likelihood was first introduced by R. A. Fisher, a geneticist and statistician, in the 1920s.

Most statisticians recommend this method, at least when the sample size is large, since the resulting estimators have certain desirable efficiency properties.

Question 32

Example 15