Nonparametric least squares estimation in derivative families

Peter Hall and Adonis Yatchew

Journal of Econometrics, 2010, vol. 157, issue 2, 362-374

Abstract: Cost function estimation often involves data on a function and a family of its derivatives. Such data can substantially improve convergence rates of nonparametric estimators. We propose series-type estimators which incorporate the various derivative data into a single nonparametric least-squares procedure. Convergence rates are obtained and it is shown that for low-dimensional cases, much of the beneficial impact is realized even if only data on ordinary first-order partials are available. In instances where root-n consistency is attained, smoothing parameters can often be chosen very easily, without resort to cross-validation. Simulations and an illustration of cost function estimation are included.

Keywords: Nonparametric; regression; Cost; and; factor; demand; estimation; Partial; derivative; data; Curse; of; dimensionality; Dimension; reduction; Rates; of; convergence; Orthogonal; series; methods; Cross-validation; Smoothing; parameter; selection (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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