IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v35y2020i4d10.1007_s00180-019-00949-0.html
   My bibliography  Save this article

Comparison among simultaneous confidence regions for nonlinear diffusion models

Author

Listed:
  • Claudia Furlan

    (University of Padova)

  • Cinzia Mortarino

    (University of Padova)

Abstract

Accuracy measures for parameter estimates represent a tricky issue in nonlinear models. Practitioners often use separate marginal confidence intervals for each parameter in place of a simultaneous confidence region (sCR). However, this can be extremely misleading due to the curvature of the parameter space of the nonlinear model. For low parameter dimensions, routines for evaluating approximate sCRs are available in the most common software programs; however, the degree of accuracy depends on the curvature of the parameter space and the sample size. Exact sCRs are computationally intensive, and for this reason, in the past, they did not receive much attention. In this paper, we perform a comparison among exact, asymptotic exact, approximate sCRs, and marginal confidence intervals. More modern regions based on bootstrap are also examined as an alternative approach (both parametric and nonparametric). Their degree of accuracy is compared with both real data and simulation results. Among the nonlinear models, in this paper, the focus is on two of the most widespread diffusion models of products and technologies, that is, the Bass and Generalized Bass models. Three different empirical studies are analyzed here. Simulation studies are also performed for lifecycles with the same diffusion characteristics as those of the empirical studies. Our results show that, as the parameter dimension increases, overlapping among the alternative sCRs reduces. The approximate sCR shows inadequate values of overlapping with the exact sCR, even for moderate parameter dimension. Bootstrap regions also exhibit good performance in describing the shape of the exact region when curvature is present, but they fail to spread up to its boundary. The coverage probability of each region is assessed with simulations. We observe that the coverage probability of the approximate sCR decreases rapidly, even for moderate parameter dimension, and it is smaller than the nominal level for bootstrap regions.

Suggested Citation

  • Claudia Furlan & Cinzia Mortarino, 2020. "Comparison among simultaneous confidence regions for nonlinear diffusion models," Computational Statistics, Springer, vol. 35(4), pages 1951-1991, December.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-019-00949-0
    DOI: 10.1007/s00180-019-00949-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-019-00949-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-019-00949-0?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. Boswijk, H. Peter & Franses, Philip Hans, 2005. "On the Econometrics of the Bass Diffusion Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 255-268, July.
    2. Eugene Demidenko, 2017. "Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 636-665, September.
    3. Withers, Christopher S. & Nadarajah, Saralees, 2012. "Improved confidence regions based on Edgeworth expansions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4366-4380.
    4. Lee, A. J. & Nyangoma, S. O. & Seber, G. A. F., 2002. "Confidence regions for multinomial parameters," Computational Statistics & Data Analysis, Elsevier, vol. 39(3), pages 329-342, May.
    5. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
    6. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    7. Renato Guseo & Alessandra Valle, 2005. "Oil and gas depletion: Diffusion models and forecasting under strategic intervention," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 375-387, December.
    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. Claudia Furlan & Cinzia Mortarino & Mohammad Salim Zahangir, 2021. "Interaction among three substitute products: an extended innovation diffusion model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 269-293, March.
    2. Yuri Peers & Dennis Fok & Philip Hans Franses, 2012. "Modeling Seasonality in New Product Diffusion," Marketing Science, INFORMS, vol. 31(2), pages 351-364, March.
    3. Tunstall, Thomas, 2015. "Iterative Bass Model forecasts for unconventional oil production in the Eagle Ford Shale," Energy, Elsevier, vol. 93(P1), pages 580-588.
    4. Franses, Ph.H.B.F., 2009. "Forecasting Sales," Econometric Institute Research Papers EI 2009-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Dalla Valle, Alessandra & Furlan, Claudia, 2011. "Forecasting accuracy of wind power technology diffusion models across countries," International Journal of Forecasting, Elsevier, vol. 27(2), pages 592-601.
    6. Singhal, Shakshi & Anand, Adarsh & Singh, Ompal, 2020. "Studying dynamic market size-based adoption modeling & product diffusion under stochastic environment," Technological Forecasting and Social Change, Elsevier, vol. 161(C).
    7. Dalla Valle, Alessandra & Furlan, Claudia, 2014. "Diffusion of nuclear energy in some developing countries," Technological Forecasting and Social Change, Elsevier, vol. 81(C), pages 143-153.
    8. Massiani, Jérôme & Gohs, Andreas, 2015. "The choice of Bass model coefficients to forecast diffusion for innovative products: An empirical investigation for new automotive technologies," Research in Transportation Economics, Elsevier, vol. 50(C), pages 17-28.
    9. Furlan, Claudia & Guidolin, Mariangela & Guseo, Renato, 2016. "Has the Fukushima accident influenced short-term consumption in the evolution of nuclear energy? An analysis of the world and seven leading countries," Technological Forecasting and Social Change, Elsevier, vol. 107(C), pages 37-49.
    10. H.P. Boswijk & D. Fok & P.-H. Franses, 2006. "A New Multivariate Product Growth Model," Tinbergen Institute Discussion Papers 06-027/4, Tinbergen Institute.
    11. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    12. Guseo, Renato & Mortarino, Cinzia & Darda, Md Abud, 2015. "Homogeneous and heterogeneous diffusion models: Algerian natural gas production," Technological Forecasting and Social Change, Elsevier, vol. 90(PB), pages 366-378.
    13. Dalla Valle, Alessandra & Furlan, Claudia, 2011. "Forecasting accuracy of wind power technology diffusion models across countries," International Journal of Forecasting, Elsevier, vol. 27(2), pages 592-601, April.
    14. Renato Guseo & Mariangela Guidolin, 2008. "Cellular automata and Riccati equation models for diffusion of innovations," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 291-308, July.
    15. Fernández-Durán, J.J., 2014. "Modeling seasonal effects in the Bass Forecasting Diffusion Model," Technological Forecasting and Social Change, Elsevier, vol. 88(C), pages 251-264.
    16. Frank M. Bass, 2004. "Comments on "A New Product Growth for Model Consumer Durables The Bass Model"," Management Science, INFORMS, vol. 50(12_supple), pages 1833-1840, December.
    17. Constanza Fosco, 2012. "Spatial Difusion and Commuting Flows," Documentos de Trabajo en Economia y Ciencia Regional 30, Universidad Catolica del Norte, Chile, Department of Economics, revised Sep 2012.
    18. Peres, Renana & Muller, Eitan & Mahajan, Vijay, 2010. "Innovation diffusion and new product growth models: A critical review and research directions," International Journal of Research in Marketing, Elsevier, vol. 27(2), pages 91-106.
    19. Franses, Philip Hans, 2006. "Forecasting in Marketing," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 18, pages 983-1012, Elsevier.
    20. Guseo, Renato, 2016. "Diffusion of innovations dynamics, biological growth and catenary function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 1-10.

    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:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-019-00949-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.