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Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions

  • Arthur Lewbel

    ()

    (Boston College)

  • Oliver Linton

    ()

    (London School of Economics)

For vectors z and w and scalar v, let r(v,z,w) be a function that can be nonparametrically estimated consistently and asymptotically normally, such as a distribution, density, or conditional mean regression function. We provide consistent, asymptotically normal nonparametric estimators for the functions G and H, where r(v,z,w)=H[vG(z),w], and some related models. This framework encompasses homothetic and homothetically separable functions, and transformed partly additive models r(v,z,w)=h[v+g(z),w] for unknown functions g and h. Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. We also provide an estimator of G that is oracle efficient, achieving the same performance as an estimator based on local least squares knowing H.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 585.

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Length: 18 pages
Date of creation: 29 Oct 2003
Date of revision: 04 Sep 2006
Handle: RePEc:boc:bocoec:585
Note: Previously circulated as "Nonparametric Estimation of Homothetic and Homothetically Separable Functions"
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  16. Tripathi, Gautam & Kim, Woocheol, 2000. "Nonparametric estimation of homogeneous function," SFB 373 Discussion Papers 2000,85, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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