Berndt–Hall–Hall–Hausman algorithm - Alchetron, the free social encyclopedia

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, β_k given by

β k + 1 = β k − λ k A k ∂ Q ∂ β ( β k ) , ,

where β k is the parameter estimate at step k, and λ k is a parameter (called step size) which partly determines the particular algorithm. For the BHHH algorithm λ_k is determined by calculations within a given iterative step, involving a line-search until a point β_k₊₁ is found satisfying certain criteria. In addition, for the BHHH algorithm, Q has the form

Q = ∑ i = 1 N Q i

and A is calculated using

A k = [ ∑ i = 1 N ∂ ln ⁡ Q i ∂ β ( β k ) ∂ ln ⁡ Q i ∂ β ( β k ) ′ ] − 1 .

In other cases, e.g. Newton–Raphson, A k can have other forms. The BHHH algorithm has the advantage that, if certain conditions apply, convergence of the iterative procedure is guaranteed.

References

Berndt–Hall–Hall–Hausman algorithm Wikipedia

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