Sobolev Estimation of Approximate Regressions

Florens, Jean-Pierre, Marc Ivaldi and Sophie Larribeau

Econometric Theory, 1996, vol. 12, issue 05, pages 753-772

Abstract: This paper focuses on the estimation of an approximated function and its derivatives. Let us assume that the data-generating process can be described by a family of regression models , where a is a multi-index of differentiation such that D th derivative of (xi) with respect to xi. The estimated model is characterized by a family D ), where D ) is the ) and such that D (Xi). Three different problems are discussed. First, the asymptotic behavior of the seemingly unrelated regression estimator of )| are introduced, and the different limits of estimated regressions characterized by these sets are proved to be equal if and only if the explanatory variables have a normal distribution. This result leads to a specification test.

Date: 1996

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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:12:y:1996:i:05:p:753-772_00

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