Bias and Consistency

Question 1

When is an estimator Unbiased

Answer 1

• An estimator is unbiased if, on average, it hits the true parameter value
• That is, the mean of the sampling distribution of the estimator is equal to the true parameter value

Question 2

When is an estimator consistent

Answer 2

• An estimator is consistent if, as the sample size increases, the estimates produced by the estimator converge to the true value of the paramter being estimated

Question 3

What is the difference between Unbiasedness and Consistency

Answer 3

• Consistency is a statement about “where the sampling distribution estimator is going” as the sample size increases
• Unbiasedness is a statement about the expected value of the sampling distribution of the estimator