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Nonparametric matching and efficient estimators of homothetically separable functions. (English) Zbl 1134.91548

Summary: 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 when \(H\) is known.

MSC:

91B82 Statistical methods; economic indices and measures
62G05 Nonparametric estimation
62P20 Applications of statistics to economics
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