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NONPARAMETRIC STUDY OF SOLUTIONS OF DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  12 December 2005

Anne Vanhems
Anne Vanhems
Affiliation:
Toulouse Business School
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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.

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 1 , February 2006 , pp. 127 - 157
Copyright
© 2006 Cambridge University Press

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