BL13

Question 1

In asymptotic/large sample analysis, 2 properties that come about?

Answer 1

1) Consistency - in large samples the estimator is equal to the true parameter with probability 1
2) Even without normality assumption (MLR5), t and F statistics have approximately f and F distributions in large samples

Question 2

What is the minimum property an estimator can have?

Answer 2

Consistency; often saves the day when unbiasedness fails

Question 3

Explain the intuition behind consistency?

Answer 3

For each n, β(hat)(j) has a probability distribution; if errors are normal, so is this prob. dist.
Since β(hat)(j) is unbiased from MLR1-4, the distribution has mean value around β(j).
If the estimator is consistent, the distribution of β(hat)(j) becomes more tightly packed around β(j) as the sample size grows, tf as n tends to infinity the distribution of β(hat)(j) collapses to a single point β(j)