56 Calculating MLE's via Iterative Algorithms To find the MLE,we usually set the score equations equal to zero and solve.The MLE usually satisfies, ∑(X;0(xn》=0 i=1 When there is no closed form solution,we can use an iterative method to solve the score equations.At the kth iteration,we have a proposed solution to the above equation,(k).We update the solution by noting that n 0= (X;d(xn》=∑(X;0)-nJ(Xn)((Xn）-8k) =1 =1 where r falls between (x)and a(k).56 Calculating MLE’s via Iterative Algorithms To find the MLE, we usually set the score equations equal to zero and solve. The MLE usually satisfies,  n i=1 ψ(Xi; ˆ θ(Xn)) = 0 When there is no closed form solution, we can use an iterative method to solve the score equations. At the kth iteration, we have a proposed solution to the above equation, θ(k). We update the solution by noting that 0 =  n i=1 ψ(Xi; ˆ θ(Xn)) =  n i=1 ψ(Xi; θ(k)) − nJ∗n(Xn)(ˆθ(Xn) − θ(k)) where θ∗n falls between ˆ θ(Xn) and θ(k)