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Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function

J.L. Horowitz (joel-horowitz@uiowa.edu)
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J.L. Horowitz: University of Iowa

Working Papers from University of Iowa, Department of Economics

Abstract: This paper is concerned with estimating the mean of a random variable Y conditional on a vector of covariates X under weak assumptions about the form of the conditional mean function. Fully nonparametric estimation is usually unattractive when X is multidimensional because estimation precision decreases rapidly as the dimension of X increases. This problem can be overcome by using dimension reduction methods such as single-index, additive, multiplicative, and partially linear models. These models are non-nested, however, so an analyst must choose among them. If an incorrect choice is made, the resulting model is misspecified and inferences based on it may be misleading. This paper describes an estimator for a new model that nests single-index, additive, and multiplicative models. The new model achieves dimension reduction without the need for choosing between single-index, additive, and multiplicative specifications. The centered, normalized estimators of the new model's unknown functions are asymptotically normally distributed. An extension of the new model nests partially linear models

Keywords: Nonparametric regression; dimension reduction; kernel estimation; single-index model; partially linear model (search for similar items in EconPapers)
JEL-codes: C13 C14 (search for similar items in EconPapers)
Pages: 42 Pages
Date: 1998-07
References: Add references at CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:uia:iowaec:98-05

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