IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n108184.html

Numerical Reduced Variable Optimization Methods via Implicit Functional Dependence with Applications

Author

Listed:
  • Christopher Gunaseelan Jesudason

Abstract

A systematic theoretical basis is developed that optimizes an arbitrary number of variables for (i) modeling data and (ii) the determination of stationary points of a function of several variables by the optimization of an auxiliary function of a single variable deemed the most significant on physical, experimental or mathematical grounds from which all the other optimized variables may be derived. Algorithms that focus on a reduced variable set avoid problems associated with multiple minima and maxima that arise because of the large numbers of parameters. For (i), both approximate and exact methods are presented, where the single controlling variable k of all the other variables P(k) passes through the local stationary point of the least squares metric. For (ii), an exact theory is developed whereby the solution of the optimized function of an independent variation of all parameters coincides with that due to single parameter optimization of an auxiliary function. The implicit function theorem has to be further qualified to arrive at this result. A nontrivial real world application of the above implicit methodology to rate constant and final concentration parameter determination is made to illustrate its utility. This work is more general than the reduction schemes for conditional linear parameters since it covers the nonconditional case as well and has potentially wide applicability.

Suggested Citation

  • Christopher Gunaseelan Jesudason, 2014. "Numerical Reduced Variable Optimization Methods via Implicit Functional Dependence with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:108184
    DOI: 10.1155/2014/108184
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/108184
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/108184?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Martin Gaynor & Nirav Mehta & Seth Richards-Shubik, 2023. "Optimal Contracting with Altruistic Agents: Medicare Payments for Dialysis Drugs," American Economic Review, American Economic Association, vol. 113(6), pages 1530-1571, June.
    2. 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.
    3. Galea, Manuel & de Castro, Mário, 2017. "Robust inference in a linear functional model with replications using the t distribution," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 134-145.
    4. Nikoloulopoulos, Aristidis K., 2023. "Efficient and feasible inference for high-dimensional normal copula regression models," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    5. 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.
    6. 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.
    7. Chien-Lin Su & Russell J. Steele & Ian Shrier, 2021. "The semiparametric accelerated trend-renewal process for recurrent event data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 357-387, July.
    8. 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.
    9. Muhammad Ahsan ul Haq & Sharqa Hashmi & Khaoula Aidi & Pedro Luiz Ramos & Francisco Louzada, 2023. "Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test," Annals of Data Science, Springer, vol. 10(2), pages 415-440, April.
    10. repec:jss:jstsof:43:i09 is not listed on IDEAS
    11. James McVittie, 2025. "Accelerated failure time and additive hazard models for combined right-censored and left-truncated right-censored failure time data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(2), pages 237-260, May.
    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. 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.
    14. 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.
    15. Sy Han Chiou & Gongjun Xu & Jun Yan & Chiung‐Yu Huang, 2018. "Semiparametric estimation of the accelerated mean model with panel count data under informative examination times," Biometrics, The International Biometric Society, vol. 74(3), pages 944-953, September.
    16. Johan Holmberg, 2024. "Earnings, labor market dynamics, and inequality in Sweden," Scandinavian Journal of Economics, Wiley Blackwell, vol. 126(3), pages 561-599, July.
    17. Wang, Zhu, 2013. "Converting Odds Ratio to Relative Risk in Cohort Studies with Partial Data Information," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i05).
    18. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    19. Holmberg, Johan, 2021. "Earnings and Labor Market Dynamics: Indirect Inference Based on Swedish Register Data," Umeå Economic Studies 984, Umeå University, Department of Economics.
    20. Martin Gaynor & Nirav Mehta & Seth Richards-Shubik, 2020. "Optimal Contracting with Altruistic Agents," University of Western Ontario, Centre for Human Capital and Productivity (CHCP) Working Papers 20203, University of Western Ontario, Centre for Human Capital and Productivity (CHCP).
    21. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:108184. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.