Week 2

Question 1

• What is a parameter?

- What is a statistic?

Answer 1

• measures used to describe a population.

- measures computed from sample data.

Question 2

What is an estimator?

Answer 2

a strategy or rule that is used to estimate a population parameter

Question 3

• What are unbiased/ biased estimators?

- What is the equation for the bias of O’

Answer 3

Let O’ be point estimator of a parameter O. O’ is said to be unbiased if E(O’) = 0. Else O’ is a biased estimator.

Question 4

-What are asymptotically unbiased estimators?

Answer 4

If B(T) of a statistic(estimator) = 0, as n –> inf. it is said to be an asymptotically unbiased estimator.

Question 5

How can the better of two estimators be chosen with variances?

Answer 5

If Var(O1) < Var(O2) to estimate O, then O1 is better than O2.

Question 6

What is the equation for Variance?

Answer 6

S^2 = sum(Xi - X’)/ n-1

Question 7

When can Mean Squared Error(MSE) be used to compare estimators?

• What is the equation for MSE of O’?
• What is the relationship between MSE, Var(O’) and B(O’)

Answer 7

When more than one estimator is available and one or more of them is not unbiased.

• MSE(O’) = E(O’-O)^2
• MSE(O’) = Var(O’) + [B(O’)]^2