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| '''BHHH''' is an [[Optimization (mathematics)|optimization]] [[algorithm]] in [[numerical optimization]] similar to [[Gauss–Newton algorithm]]. It is an [[Acronym and initialism|acronym]] of the four originators: Berndt, B. Hall, R. Hall, and [[Jerry Hausman]].
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| ==Usage==
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| If a [[nonlinear]] model is fitted to the [[data]] one often needs to estimate [[coefficient]]s through [[Optimization (mathematics)|optimization]]. A number of optimisation algorithms have the following general structure. Suppose that the function to be optimized is ''Q''(''β''). Then the algorithms are iterative, defining a sequence of approximations, ''β<sub>k</sub>'' given by
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| :<math>\beta_{k+1}=\beta_{k}-\lambda_{k}A_{k}\frac{\partial Q}{\partial \beta}(\beta_{k}),</math>,
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| where <math>\beta_{k}</math> is the parameter estimate at step k, and <math>\lambda_{k}</math> is a parameter (called step size) which partly determines the particular algorithm. For the BHHH algorithm ''λ<sub>k</sub>'' is determined by calculations within a given iterative step, involving a line-search until a point ''β<sub>k''+1</sub> is found satisfying certain criteria. In addition, for the BHHH algorithm, ''Q'' has the form
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| :<math>Q = \sum_{i=1}^{N} Q_i</math>
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| and ''A'' is calculated using
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| :<math>A_{k}=\left[\sum_{i=1}^{N}\frac{\partial \ln Q_i}{\partial \beta}(\beta_{k})\frac{\partial \ln Q_i}{\partial \beta}(\beta_{k})'\right]^{-1} .</math>
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| In other cases, e.g. [[Newton-Raphson]], <math>A_{k}</math> can have other forms. The BHHH algorithm has the advantage that, if certain conditions apply, convergence of the iterative procedure is guaranteed.{{cn|date=March 2013}}
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| ==Literature==
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| *Berndt, E., B. Hall, R. Hall, and J. Hausman, (1974), [http://elsa.berkeley.edu/~bhhall/papers/BerndtHallHallHausman74.pdf “Estimation and Inference in Nonlinear Structural Models”], ''Annals of Economic and Social Measurement'', 3, 653–665.
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| *Luenberger, D. (1972), ''Introduction to Linear and Nonlinear Programming'', Addison Wesley, Reading Massachusetts.
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| *Gill, P., W. Murray, and M. Wright, (1981), ''Practical Optimization'', Harcourt Brace and Company, London
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| *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.
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| {{DEFAULTSORT:Bhhh Algorithm}}
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| [[Category:Econometrics]]
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| [[Category:Optimization algorithms and methods]]
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Wilber Berryhill is the title his parents gave him and he completely digs that title. Some time in the past he chose to live in North Carolina and he doesn't plan on changing it. I am presently a travel agent. To climb is something I truly appreciate performing.
Here is my homepage ... online psychics (click the next internet page)