Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function
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
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|Date of creation:||Jul 1998|
|Date of revision:|
|Contact details of provider:|| Postal: University of Iowa, Department of Economics, Henry B. Tippie College of Business, Iowa City, Iowa 52242|
Phone: (319) 335-0829
Fax: (319) 335-1956
Web page: http://tippie.uiowa.edu/economics/
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