Estimation ofβoβ1β2r…βk Maximum likelihood a Assume G to be independent identically distributed with normal distribution of zero mean and variance o2, denote the normal density for e be f)=f(yβo-βX1阝2x2…x) normal density a Choose bor b1, b2,., bk to maximize the joint likelihood L(bo,b1,b2…,b)=f(e1)*fe2)*,*f(e f(e)=f(y-bo-b1X1-b2X2-.-bk Xx) Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson11-10Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson11-10 Estimation of b0 , b1 , b2 ,…, bk Maximum Likelihood ◼ Assume ei to be independent identically distributed with normal distribution of zero mean and variance s2 . Denote the normal density for e be ◼ f(e)=f(y-b0 -b1x1 -b2x2 -…-bkxk ) f(e)= f(y-b0 -b1x1 -b2x2 -…-bkxk ) normal density ◼ Choose b0 , b1 , b2 , …, bk to maximize the joint likelihood: ◼ L(b0 , b1 , b2 , …, bk ) = f(e1 )*f(e2 )*…*f(en )