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nlr

swMATH ID: 5244
Software Authors: Bunch, David S.; Gay, David M.; Welsch, Roy E.
Description: Algorithm 717: Subroutines for maximum likelihood and quasi-likelihood estimation parameters in nonlinear regression models We present Fortran 77 subroutines that solve statistical parameter estimation problems for general nonlinear models, e.g., nonlinear least squares, maximum likelihood, maximum quasi-likelihood, generalized nonlinear least squares, and some robust fitting problems. The accompanying test examples include members of the generalized linear model family, extensions using nonlinear predictors (“nonlinear GLIM”), and probabilistic choice models, such as linear-in-parameter multinomial probit models. The basic method, a generalization of the NL2SOL algorithm for nonlinear least squares, employs a model/trust-region scheme for computing trial steps, exploits special structure by maintaining a secant approximation to the second-order part of the Hessian, and adaptively switches between a Gauss-Newton and an augmented Hessian approximation. Gauss-Newton steps are computed using a corrected seminormal equations approach. The subroutines include variants that handle simple bounds on the parameters, and that compute approximate regression diagnostics.
Homepage: http://dl.acm.org/citation.cfm?doid=151271.151279
Keywords: statistical parameter estimation; nonlinear models; nonlinear least squares; maximum likelihood; maximum quasi-likelihood; robust fitting; test examples; model/trust-region scheme; Gauss-Newton; regression
Related Software: NL2SOL; RODAS; bootstrap; Algorithm 611; CVODE; TRON; CUTEr; COLNEW; ADOL-C; AS 183; Algorithm 814; Excel; Algorithm 719; Algorithm 679; Algorithm 524; GSL; MersenneTwister; KELLEY; mctoolbox; SPRNG
Cited in: 9 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Algorithm 717: Subroutines for maximum likelihood and quasi-likelihood estimation parameters in nonlinear regression models. Zbl 0889.65149
Bunch, David S.; Gay, David M.; Welsch, Roy E.
1993
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Cited by 22 Authors

2 Džeroski, Sašo
2 Jackiewicz, Zdzislaw
2 Mittelmann, Hans Detlef
2 Todorovski, Ljupčo
1 Altman, Micah
1 Arora, Nikhil
1 Biegler, Lorenz T.
1 Bridewell, Will
1 Bunch, David S.
1 Butcher, John C.
1 Fadel, James G.
1 Gay, David M.
1 Gill, Jeff
1 Grechanovsky, Eugene
1 Langley, Pat
1 Mayer, David W.
1 McDonald, Michael P.
1 Mcphee, Malcolm
1 Oltjen, Jim
1 Pinsker, Ilia
1 Sainz, Roberto
1 Welsch, Roy E.
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Cited in 7 Serials

2 Journal of Computational and Applied Mathematics
1 ACM Transactions on Mathematical Software
1 Mathematics and Computers in Simulation
1 Machine Learning
1 Computational Statistics and Data Analysis
1 Computational Optimization and Applications
1 Wiley Series in Probability and Statistics
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Cited in 9 Fields

5 Numerical analysis (65-XX)
4 Statistics (62-XX)
3 Biology and other natural sciences (92-XX)
2 General and overarching topics; collections (00-XX)
2 Ordinary differential equations (34-XX)
2 Computer science (68-XX)
1 Operations research, mathematical programming (90-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Systems theory; control (93-XX)

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