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date: 22 August 2019

Abstract and Keywords

Much applied research in statistics, economics, and other fields is concerned with estimating a conditional mean or quantile function. Often it is assumed that this function is known up to a finite-dimensional parameter that can be estimated by least squares or other familiar methods. However, a parametric model is usually arbitrary and can be highly misleading if it is misspecified. Fully nonparametric estimation is an alternative approach that essentially eliminates the possibility of misspecification, but the curse of dimensionality makes nonparametric estimation infeasible with samples of practical size when the explanatory variable is multidimensional. This chapter reviews methods for estimating a class of models, called nonparametric additive models, that make assumptions that are stronger than those of fully nonparametric methods but much weaker than those of parametric methods. Under mild assumptions, nonparametric additive models avoid the curse of dimensionality but are more flexible than parametric models. This makes nonparametric additive models attractive for applied research. This chapter explains what nonparametric additive models are and describes methods for estimating them. The usefulness of these models is illustrated with an empirical example.

Keywords: nonparametric estimation, curse of dimensionality, dimension reduction

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