Consider the problem of minimizing the sum of squared residuals subject to the constraint that Rb = r, where R is q × ( k + 1) with rank cj. Let 11eb9b5b_3f70_8544_bf3e_1bdb7324c8da_SM2686_11 be the value of b that solves the constrained minimization problem. a. Show that the Lagrangian for the minimization problem is L(b , ) = ( Y- Xb ) ' ( Y-Xb ) + ' ( Rb - r ), where is a q × 1 vector of Lagrange multipliers. b. Show that 11eb9b5b_3f70_ac55_bf3e_9dbf756f469f_SM2686_11 c. Show that 11eb9b5b_3f70_ac56_bf3e_5b70b5ec503c_SM2686_11 11eb9b5b_3f70_d367_bf3e_9dc2b2f2ce8c_SM2686_11 d. Show that F in Equation (18.36) is equivalent to the homoskeskasticity-only F -statistic in Equation (7.13). 11eb9b5b_3f71_2188_bf3e_57537bbc5315_SM2686_00 11eb9b5b_3f71_4899_bf3e_5d5895789665_SM2686_00

Introduction to Econometrics 3rd Edition by James Stock, James Stock

النسخة 3الرقم المعياري الدولي: 978-9352863501

Introduction to Econometrics 3rd Edition by James Stock, James Stock

النسخة 3الرقم المعياري الدولي: 978-9352863501

تمرين 22

Consider the problem of minimizing the sum of squared residuals subject to the constraint that Rb = r, where R is q × ( k + 1) with rank cj. Let

be the value of b that solves the constrained minimization problem.
a. Show that the Lagrangian for the minimization problem is L(b , ) = ( Y- Xb ) ' ( Y-Xb ) + ' ( Rb - r ), where is a q × 1 vector of Lagrange multipliers.
b. Show that

c. Show that

d. Show that F in Equation (18.36) is equivalent to the homoskeskasticity-only F -statistic in Equation (7.13).

التوضيح

موثّق

a) The minimization is However it is co...