IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v81y2011i9p1795-1841.html
   My bibliography  Save this article

Comparingparameter choice methods for regularization of ill-posed problems

Author

Listed:
  • Bauer, Frank
  • Lukas, Mark A.

Abstract

In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing parameter choice methods, and evaluates and compares them in a large simulation study for spectral cut-off and Tikhonov regularization. The test cases cover a wide range of linear inverse problems with both white and colored stochastic noise. The results show some marked differences between the methods, in particular, in their stability with respect to the noise and its type. We conclude with a table of properties of the methods and a summary of the simulation results, from which we identify the best methods.

Suggested Citation

  • Bauer, Frank & Lukas, Mark A., 2011. "Comparingparameter choice methods for regularization of ill-posed problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1795-1841.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:9:p:1795-1841
    DOI: 10.1016/j.matcom.2011.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475411000607
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2011.01.016?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cummins D. J & Filloon T. G. & Nychka D., 2001. "Confidence Intervals for Nonparametric Curve Estimates: Toward More Uniform Pointwise Coverage," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 233-246, March.
    2. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Petojević, Zorana & Gospavić, Radovan & Todorović, Goran, 2018. "Estimation of thermal impulse response of a multi-layer building wall through in-situ experimental measurements in a dynamic regime with applications," Applied Energy, Elsevier, vol. 228(C), pages 468-486.
    2. Hohage, Thorsten & Maréchal, Pierre & Simar, Léopold & Vanhems, Anne, 2024. "A Mollifier Approach To The Deconvolution Of Probability Densities," Econometric Theory, Cambridge University Press, vol. 40(2), pages 320-359, April.
    3. Tarik Chakkour, 2017. "Some Notes about the Continuous-in-Time Financial Model," Post-Print hal-01584982, HAL.
    4. Naik, Shraddha M. & Jagannath, Ravi Prasad K. & Kuppili, Venkatanareshbabu, 2020. "Fractional Tikhonov regularization to improve the performance of extreme learning machines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    5. Mohanrasu, S.S. & Janani, K. & Rakkiyappan, R., 2024. "A COPRAS-based Approach to Multi-Label Feature Selection for Text Classification," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 3-23.

    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. Stevanovic Dalibor, 2016. "Common time variation of parameters in reduced-form macroeconomic models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(2), pages 159-183, April.
    2. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    3. A. Fadlelmawla & M. Al-Otaibi, 2005. "Analysis of the Water Resources Status in Kuwait," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 19(5), pages 555-570, October.
    4. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    5. Duan, Jinyun & Li, Chenwei & Xu, Yue & Wu, Chia-Huei, 2017. "Transformational leadership and employee voice behavior: a Pygmalion mechanism," LSE Research Online Documents on Economics 68035, London School of Economics and Political Science, LSE Library.
    6. Hota, Monali & Bartsch, Fabian, 2019. "Consumer socialization in childhood and adolescence: Impact of psychological development and family structure," Journal of Business Research, Elsevier, vol. 105(C), pages 11-20.
    7. Abernethy, Margaret A. & Vagnoni, Emidia, 2004. "Power, organization design and managerial behaviour," Accounting, Organizations and Society, Elsevier, vol. 29(3-4), pages 207-225.
    8. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    9. Peter Burnell, 2008. "From Evaluating Democracy Assistance to Appraising Democracy Promotion," Political Studies, Political Studies Association, vol. 56(2), pages 414-434, June.
    10. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    11. Mammassis, Constantinos S. & Kostopoulos, Konstantinos C., 2019. "CEO goal orientations, environmental dynamism and organizational ambidexterity: An investigation in SMEs," European Management Journal, Elsevier, vol. 37(5), pages 577-588.
    12. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    13. Viren Swami & Phik-Wern Loo & Adrian Furnham, 2010. "Public Knowledge and Beliefs About Depression Among Urban and Rural Malays in Malaysia," International Journal of Social Psychiatry, , vol. 56(5), pages 480-496, September.
    14. Jugend, Daniel & da Silva, Sérgio Luis & Salgado, Manoel Henrique & Miguel, Paulo Augusto Cauchick, 2016. "Product portfolio management and performance: Evidence from a survey of innovative Brazilian companies," Journal of Business Research, Elsevier, vol. 69(11), pages 5095-5100.
    15. Ruiwei Jiang & Siqian Shen & Yiling Zhang, 2017. "Integer Programming Approaches for Appointment Scheduling with Random No-Shows and Service Durations," Operations Research, INFORMS, vol. 65(6), pages 1638-1656, December.
    16. Mínguez, R. & García-Bertrand, R., 2016. "Robust transmission network expansion planning in energy systems: Improving computational performance," European Journal of Operational Research, Elsevier, vol. 248(1), pages 21-32.
    17. Jenny Carolina Saldana Cortés, 2011. "Programación semidefinida aplicada a problemas de cantidad económica de pedido," Documentos CEDE 8735, Universidad de los Andes, Facultad de Economía, CEDE.
    18. Ian Maitland & Mitsuhiro Umezu, 2006. "An Evaluation of Japan's Stakeholder Capitalism," Journal of Private Enterprise, The Association of Private Enterprise Education, vol. 22(Spring 20), pages 131-164.
    19. Mikhail A. Sokolovskiy & Xavier J. Carton & Boris N. Filyushkin, 2020. "Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 1: Point-Vortex Approach," Mathematics, MDPI, vol. 8(8), pages 1-13, July.
    20. Craig Loschmann & Özge Bilgili & Melissa Siegel, 2019. "Considering the benefits of hosting refugees: evidence of refugee camps influencing local labour market activity and economic welfare in Rwanda," IZA Journal of Migration and Development, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 9(1), pages 1-23, December.

    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:eee:matcom:v:81:y:2011:i:9:p:1795-1841. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.