MLE_Lecture 6 - Lecture 6 Numerical Optimization Techniques Want to maximize or minimize the(possibly nonlinear objective function F which is usually

# MLE_Lecture 6 - Lecture 6 Numerical Optimization Techniques...

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Lecture 6 Numerical Optimization Techniques Want to maximize or minimize the (possibly nonlinear) objective function ( ) F θ , which is usually log likelihood function. 3 parts to numerical search algorithms: (1) obtaining initial starting values for the parameters, say 0 θ (2) updating the candidate value for θ (3) determining when the optimum has been reached. If the objective function is globally concave so there is a unique maximum, then any algorithm which improves the parameter vector at each iteration will eventually find the maximum (example: logit likelihood function). If the function ( ) F θ is not globally concave, then different algorithms may find different local maxima. However, all iterative algorithms will suffer from the same problem of not being able to distinguish between a local and a global maximum. The main thing that distinguishes different algorithms is how fast they find the maximum. One algorithm may be better in one case but not in another. Performance is often case specific. Numerical optimization algorithms can be broadly classified into two types: first derivative methods and second derivative methods. First derivative methods form candidates based on using only the first derivative of the objective function. Second derivative methods form candidates based on using the second derivative of the objective function. ———————————————————————————————————— Ref.: EVIEWS User’s Manual pp. 619-622.

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