Point Estimation

Question 1

Define a point estimator

Answer 1

Note: random variables are called estimators, the specific value for a specific sample is the estimate

Question 2

Describe unbiasedness as a property when measuring the effectiveness of an estimator

Answer 2

Question 3

Describe consistency as a property when measuring the effectiveness of an estimator

Answer 3

Question 4

Describe efficiency as a property when measuring the effectiveness of an estimator

Answer 4

Question 5

Describe standard error as a property when measuring the effectiveness of an estimator

Answer 5

Question 6

Describe the Least Squares Estimator (LSE) method of estimation

Answer 6

• Minimise the sum of (X_i-E(X))²
• Derive this sum wrt the parameter
• Set the differential to 0

Question 7

Describe the Method of moments estimators (MME) method of estimation

Answer 7

• Determine the number of unknown parameters (r)
• Express r parameters as population moments (θ)
• Express r parameters as sample moments (θˆ)
• Express θ^{^} as functions of the sample moments

Question 8

Define population moments

Answer 8

Question 9

Define sample moments

Answer 9

Question 10

Define the likelihood function

Answer 10

Question 11

Describe the Maximum Likelihood Estimators (MLE) method of estimation

Answer 11

Differentiate L(θ) or lnL(wrt θ and set the derivative to 0

Question 12

Describe an alternative method for working out the MLE

Answer 12

Differentiate l(θ) wrt θ and set the derivative to 0