Let sigma=1 and consider the special case of only two observations (n=2). Write down a formula for the mean squared error E[(delta_1 hat-delta_1)^2] as a function of t_1 and t_2. Enter t_1 for t_1 and t_2 for t_2.

Answer 1

In the case of only two observations (n=2), the mean squared error can be calculated using the formula:

E[(delta_1 hat - delta_1)^2] = Var(delta_1 hat) + (Bias(delta_1 hat))^2

Since we are given that sigma=1, the variance, Var(delta_1 hat), can be calculated as:

Var(delta_1 hat) = sigma^2 / n = 1/2 = 0.5

Bias(delta_1 hat) represents the bias of the estimator and, in this case, will depend on the specific estimators used for delta_1 hat. Without further information, it is not possible to determine the exact value of Bias(delta_1 hat) and thus the mean squared error. Therefore, we cannot provide a specific formula in terms of t_1 and t_2 without additional information on the estimators employed.