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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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    5. 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.
    6. Withers, Christopher S. & Nadarajah, Saralees, 2012. "Improved confidence regions based on Edgeworth expansions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4366-4380.
    7. 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.
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