Consider the simple regression yt = xt + 1 where E p[ | x] = 0 and

Consider the simple regression yt = βxt + ε1 where E p[ε | x] = 0 and E [ε2 | x ] = σ2

(a) What is the minimum mean squared error linear estimator of β? Choose e to minimize Var [β] + [E(β ?? β)]2. The answer is a function of the unknown parameters].

(b) For the estimator in part a, show that ratio of the mean squared error of β to that of the ordinary least squares estimator b is Note that τ is the square of the population analog to the ??t ratio?? for testing the hypothesis that β = 0, which is given in (4-14). How do you interpret the behavior of this ratio as τ ?? ???

Transcribed Image Text:

MSE [B] MSE [b] 7² (1+T²)' where T2 = [0²/X'X]