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BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function

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  • Varadhan, Ravi
  • Gilbert, Paul

Abstract

We discuss R package BB, in particular, its capabilities for solving a nonlinear system of equations. The function BBsolve in BB can be used for this purpose. We demonstrate the utility of these functions for solving: (a) large systems of nonlinear equations, (b) smooth, nonlinear estimating equations in statistical modeling, and (c) non-smooth estimating equations arising in rank-based regression modeling of censored failure time data. The function BBoptim can be used to solve smooth, box-constrained optimization problems. A main strength of BB is that, due to its low memory and storage requirements, it is ideally suited for solving high-dimensional problems with thousands of variables.

Suggested Citation

  • Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
  • Handle: RePEc:jss:jstsof:v:032:i04
    DOI: http://hdl.handle.net/10.18637/jss.v032.i04
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    References listed on IDEAS

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    1. Ravi Varadhan & Christophe Roland, 2008. "Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 335-353.
    2. Zhezhen Jin, 2003. "Rank-based inference for the accelerated failure time model," Biometrika, Biometrika Trust, vol. 90(2), pages 341-353, June.
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    Cited by:

    1. Robert Vlacuha & Boris Frankovic, 2015. "The Calibration of Weights by Calif Tool in the Practice of the Statistical Office of the Slovak Republic," Romanian Statistical Review, Romanian Statistical Review, vol. 63(2), pages 153-164, June.
    2. HaiYing Wang & Nancy Flournoy & Eloi Kpamegan, 2014. "A new bounded log-linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 695-720, July.
    3. Nathan H. Miller & Matthew Osborne, 2014. "Spatial differentiation and price discrimination in the cement industry: evidence from a structural model," RAND Journal of Economics, RAND Corporation, vol. 45(2), pages 221-247, June.
    4. OUATTARA, Aboudou & DE LA BRUSLERIE, Hubert, 2015. "The term structure of psychological discount rate: characteristics and functional forms," MPRA Paper 75111, University Library of Munich, Germany.
    5. repec:eee:jmvana:v:160:y:2017:i:c:p:134-145 is not listed on IDEAS
    6. Daniel Alai & Zinoviy Landsman & Michael Sherris, 2012. "Lifetime Dependence Modelling using the Truncated Multivariate Gamma Distribution," Working Papers 201211, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    7. Gzyl, Henryk & ter Horst, Enrique & Molina, German, 2015. "A spectral measure estimation problem in rheology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 129-133.
    8. Ola L{o}vsletten & Martin Rypdal, 2012. "A multifractal approach towards inference in finance," Papers 1202.5376, arXiv.org.
    9. Predrag M. Popović & Miroslav M. Ristić & Aleksandar S. Nastić, 2016. "A geometric bivariate time series with different marginal parameters," Statistical Papers, Springer, vol. 57(3), pages 731-753, September.
    10. Gauss M. Cordeiro & Maria do Carmo S. Lima & Antonio E. Gomes & Cibele Q. da-Silva & Edwin M. M. Ortega, 2016. "The gamma extended Weibull distribution," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-19, December.
    11. Božidar Popović & Saralees Nadarajah & Miroslav Ristić, 2013. "A new non-linear AR(1) time series model having approximate beta marginals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 71-92, January.
    12. Alai, Daniel H. & Landsman, Zinoviy & Sherris, Michael, 2013. "Lifetime dependence modelling using a truncated multivariate gamma distribution," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 542-549.
    13. Varadhan, Ravi, 2014. "Numerical Optimization in R: Beyond optim," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i01).
    14. José-Alberto Guerra & Myra Mohnen, 2017. "Multinomial choice with social interactions: occupations in Victorian London," DOCUMENTOS CEDE 015667, UNIVERSIDAD DE LOS ANDES-CEDE.

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