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Berndt–Hall–Hall–Hausman algorithm
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Berndt–Hall–Hall–Hausman algorithm : ウィキペディア英語版
Berndt–Hall–Hall–Hausman algorithm
The Berndt–Hall–Hall–Hausman (BHHH) algorithm is a numerical optimization algorithm similar to the Gauss–Newton algorithm. It is named after the four originators: Ernst R. Berndt, B. Hall, Robert Hall, and Jerry Hausman.
==Usage==
If a nonlinear model is fitted to the data one often needs to estimate coefficients through 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, ''βk'' given by
:\beta_=\beta_-\lambda_A_\frac(\beta_),,
where \beta_ is the parameter estimate at step k, and \lambda_ is a parameter (called step size) which partly determines the particular algorithm. For the BHHH algorithm ''λk'' is determined by calculations within a given iterative step, involving a line-search until a point ''βk''+1 is found satisfying certain criteria. In addition, for the BHHH algorithm, ''Q'' has the form
:Q = \sum_^ Q_i
and ''A'' is calculated using
:A_=\left(Newton–Raphson, A_ can have other forms. The BHHH algorithm has the advantage that, if certain conditions apply, convergence of the iterative procedure is guaranteed.

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