Take the normal regression model Y X0e with e j X N(0,2) where we know the MLE equals the least squares estimators b

Take the normal regression model Y Æ X0¯Åe with e j X » N(0,¾2) where we know the MLE equals the least squares estimators b¯ and b¾

2.

(a) Describe the parametric regression bootstrap for this model. Show that the conditional distribution of the bootstrap observations is Y ¤

i j Fn »N

¡

X0 i

b¯,b¾

2¢

.

(b) Show that the distribution of the bootstrap least squares estimator is b¯¤ j Fn »N ³
b¯, ¡
X 0X ¢¡1b¾
2 ´
.

(c) Show that the distribution of the bootstrap t-ratio with a homoskedastic standard error is T ¤ »
tn¡k .