QA5 - Sample Moments

Question 1

Explain the difference between a population moment and a sample moment

Answer 1

Population moment is the true moment, population is that estimated from a sample

Question 2

Describe the bias of an estimator and explain what the bias measures

Answer 2

Bias is zero if E(mu_hat) = mu, measures difference between the expected value of the estimator and the population value estimated

Question 3

Explain what is meant by the statement that the mean estimator is BLUE

Answer 3

Best linear unbiased estimator, i.e. estimator that has the smallest variance

Question 4

Describe the consistency of an estimator and explain the usefulness of this concept

Answer 4

Consistent when the variance of an estimator tends to zero as n increases (asymptotically unbiased)

Question 5

Explain how the Law of Large Numbers and Central Limit Theorem (CLT) apply to the sample mean

Answer 5

LNN says as n increases, mu_hat tends towards mu
CLT says as n increases, mu tends towards normal distribution mean mu and variance sigma^2 / n

Question 6

Explain how coskewness and cokurtosis are related to skewness and kurtosis

Answer 6

Two measures of coskewness, measures sensitivity of one variable taking a large directional value given a large magnitude of the other

Three measures of cokurtosis, measuring strength of link between covariances and dependence in signed extremes