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Nonparametric Estimation of a Generalized Additive Model With an Unknown Link Function
Author(s) -
Horowitz Joel L.
Publication year - 2001
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00200
Subject(s) - nonparametric statistics , citation , function (biology) , link (geometry) , estimation , mathematical economics , econometrics , library science , sociology , computer science , mathematics , economics , combinatorics , management , evolutionary biology , biology
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 o f X increases. This problem can be overcome by using dimension reduction methods s uch as single-index, additive, multiplicative, and partially linear models. These models are non-nested, ho wever, 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 f or a new model t hat 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.