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Specification testing for ordinary differential equation models with fixed design and applications to COVID-19 epidemic models

Author

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  • Liu, Ran
  • Zhu, Lixing

Abstract

Checking the models about the ongoing Coronavirus Disease 2019 (COVID-19) pandemic is an important issue. Some famous ordinary differential equation (ODE) models, such as the SIR and SEIR models have been used to describe and predict the epidemic trend. Still, in many cases, only part of the equations can be observed. A test is suggested to check possibly partially observed ODE models with a fixed design sampling scheme. The asymptotic properties of the test under the null, global and local alternative hypotheses are presented. Two new propositions about U-statistics with varying kernels based on independent but non-identical data are derived as essential tools. Some simulation studies are conducted to examine the performances of the test. Based on the available public data, it is found that the SEIR model, for modeling the data of COVID-19 infective cases in certain periods in Japan and Algeria, respectively, maybe not be appropriate by applying the proposed test.

Suggested Citation

  • Liu, Ran & Zhu, Lixing, 2023. "Specification testing for ordinary differential equation models with fixed design and applications to COVID-19 epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322001967
    DOI: 10.1016/j.csda.2022.107616
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    References listed on IDEAS

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    1. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    2. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(6), pages 1016-1041, December.
    3. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    4. Giles Hooker, 2009. "Forcing Function Diagnostics for Nonlinear Dynamics," Biometrics, The International Biometric Society, vol. 65(3), pages 928-936, September.
    5. repec:bla:biomet:v:71:y:2015:i:4:p:1176-1184 is not listed on IDEAS
    6. Pascal Lavergne & Valentin Patilea, 2012. "One for All and All for One: Regression Checks With Many Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 41-52.
    7. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    8. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
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