BHHH algorithm

BHHH is an optimization algorithm in econometrics similar to Gauss–Newton algorithm. It is an acronym of the four originators: Berndt, B. Hall, R. Hall, and Jerry Hausman.

Usage

If a nonlinear model is fitted to the data one often needs to estimate coefficients through optimization. In general,where is the coefficient at step k, $lambda\_\{k\}$ is a parameter, $Q\; =\; sum\_\{i=1\}^\{N\}\; Q\_i$ is the objective function (the negative of the likelihood function) and in the case of BHHH. In other cases, e.g. Newton-Raphson, $A\_\{k\}$ can have other forms.

Literature

*Berndt, E., B. Hall, R. Hall, and J. Hausman, (1974), “Estimation and Inference in Nonlinear Structural Models”, Annals of Social Measurement, Vol. 3, 653-665.
*Luenberger, D. (1972), Introduction to Linear and Nonlinear Programming, Addison Wesley, Reading Massachusetts.
*Gill, P., W. Murray, and M. Wright, (1981), Practical Optimization, Harcourt Brace and Company, London
*Sokolov, S.N., and I.N. Silin (1962), “Determination of the coordinates of the minima of functionals by the linearization method”, Joint Institute for Nuclear Research preprint D-810, Dubna.