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Nonparametric Study Of Solutions Of Differential Equations

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  • Vanhems, Anne

Abstract

The solution of differential equations lies at the heart of many problems in structural economics. In econometrics the general nonparametric analysis of consumer welfare is historically the most obvious application, but there are also many applications in finance and other fields. This work considers the general nonparametric form for these problems and identification conditions. It derives a kernel-based estimator and shows consistency and asymptotic normality.In particular, the link with inverse problems allows us to define it in terms of a well-posed inverse problem and to stress the regularity properties of the estimated solution.I thank Jean-Pierre Florens, Richard Blundell, Eric Renault, and Christine Thomas-Agnan for stimulating conversations, suggestions, and advice. I am very grateful to Oliver Linton and two anonymous referees for most helpful comments.

Suggested Citation

  • Vanhems, Anne, 2006. "Nonparametric Study Of Solutions Of Differential Equations," Econometric Theory, Cambridge University Press, vol. 22(1), pages 127-157, February.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:01:p:127-157_06
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    Cited by:

    1. Anne Vanhems & Jean-Michel Loubes, 2004. "Saturation spaces for regularization methods in inverse problems," Econometric Society 2004 North American Summer Meetings 380, Econometric Society.
    2. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    3. Stefan Hoderlein & Anne Vanhems, 2018. "Estimating the distribution of welfare effects using quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 52-72, January.
    4. Berenguer, M.I. & Gámez, D. & Kunze, H. & La Torre, D. & Ruiz Galán, M., 2024. "Solving direct and inverse problems for Fredholm-type integro-differential equations with application to pollution diffusion modeling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 394-404.

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