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Introduction to Econometrics 3rd Edition by James Stock, Mark Watson
Edition 3ISBN: 978-9352863501Introduction to Econometrics 3rd Edition by James Stock, Mark Watson
Edition 3ISBN: 978-9352863501 Exercise 1
Suppose that C is an n × n symmetric idempotent matrix with rank r and let V ~ N (0 n , I n ).
a. Show that C = AA ', where A is n × r with A'A = I r. ( Hint: C is possintive semidefinite and can be written as Q Q as explained in Appendix 18.1.)
b. Show that A'V ~ N ( 0 r , I r ).
c. Show that V'CV ~ r 2
a. Show that C = AA ', where A is n × r with A'A = I r. ( Hint: C is possintive semidefinite and can be written as Q Q as explained in Appendix 18.1.)
b. Show that A'V ~ N ( 0 r , I r ).
c. Show that V'CV ~ r 2
Explanation
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a) Since C is semidefinite and positive
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Introduction to Econometrics 3rd Edition by James Stock, Mark Watson
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