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Berndt–Hall–Hall–Hausman Algorithm
The Berndt–Hall–Hall–Hausman (BHHH) algorithm is a numerical optimization algorithm similar to the Newton–Raphson algorithm, but it replaces the observed negative Hessian matrix with the outer product of the gradient. This approximation is based on the information matrix equality and therefore only valid while maximizing a likelihood function. The BHHH algorithm is named after the four originators: Ernst R. Berndt, Bronwyn 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 optimization 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 algo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Numerical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Optimization problems can be divided into two categories, depending on whether the variables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |