Advanced Econometrics Takeshi Amemiya
Methods of Iteration
Be it for the maximum likelihood or the nonlinear least squares estimator, we cannot generally solve the equation of the form (4.1.9) explicitly for 0. Instead, we must solve it iteratively: Start from an initial estimate of 0 (say 0,) and obtain a sequence of estimates {§„} by iteration, which we hope will converge to the global maximum (or minimum) of QT or at least a root of Eq. (4.1.9). Numerous iterative methods have been proposed and used. In this section we shall discuss several well-known methods that are especially suitable for obtaining the maximum likelihood and the nonlinear least squares estimator. Many of the results of this section can be found in Goldfeld and Quandt (1972), Draper and Smith (1981), or, more extensively, in Quandt (1983).
