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In a situation where the first derivative of the log likelihood function is available, an efficient method of finding the maximum of the pseudo log-likelihood equation is one developed by Bernt, Hall, Hall and Hausman [BHHH] (1974) based on the Newton-Raphson algorithm. This method is based on starting from some easy but imprecise estimate of the Maximum Likelihood estimators, then taking a succession of ‘steps’ based on the value of the first derivatives until a solution is found.
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