Example: Generalized method of moments If v>4, the population fourth moment of the t-distribution is 4=E(y) (y-2)1 If we want to choose v to match both moment, we have following minimization problem where Q(,yrs=gwg } 4T (v-2)v-4) W is 2x2 positive define symmetric matrix reflecting the importance given to matching each of the momentsExample:Generalized Method of Moments • If , the population fourth moment of the t-distribution is • If we want to choose v to match both moment, we have following minimization problem • where • W is positive define symmetric matrix reflecting the importance given to matching each of the moments ν > 4 ( 2)( 4 ) 3 ( ) 2 4 4 − − = = v v v E y µ t { } Q v y T y g Wg v ( , ,..., ) ' min 1 = ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − − − ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − − = ( 2)( 4 ) 3 ˆ 2 ˆ 2 4, 2, v v v v v g T T µ µ 2 × 2