Explanation:
D is correct. The bias of an estimator is defined as:
Where is the true value of the parameter that we are estimating. It measures the difference between the expected value of the estimator and the population value being estimated.
A and C are incorrect. As explained above, bias is calculated as the difference between the expected value of the estimator and the population value being estimated.
B is incorrect. When the expected value of the estimator is equal to the true population value being estimated, bias is zero.
Learning Objective: Describe the bias of an estimator and explain what the bias measures.
Reference: Global Association of Risk Professionals. Quantitative Analysis. New York, NY: Pearson, 2023, Chapter 5, Sample Moments [QA-5].
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Q-79. A financial risk analyst at a real estate firm is preparing a report on housing prices. The analyst compiles the summary statistics for a dataset with 25 observations and decides to use bias-corrected estimators of the parameters due to the sample size. Which of the following correctly describes the bias of an estimator?
A
The bias is typically calculated by taking the square of the deviation between two mean estimators.
B
The bias is greatest when the expected value of the estimator is equal to the true population value being estimated.
C
The bias is equal to the expected value of the estimator divided by the population value being estimated.
D
The bias is the difference between the expected value of an estimator and the true value of the population parameter.
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