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

Author

Listed:
  • Horowitz, J.L.

    (University of Iowa)

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

Suggested Citation

  • Horowitz, J.L., 1998. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Working Papers 98-05, University of Iowa, Department of Economics.
    • Handle: RePEc:uia:iowaec:98-05
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    Citations

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    Cited by:

    1. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    2. Arthur Lewbel & Linton, Oliver Linton, 1998. "Nonparametric Censored Regression," Cowles Foundation Discussion Papers 1186, Cowles Foundation for Research in Economics, Yale University.
    3. Joris Pinkse, 2000. "Feasible Multivariate Nonparametric Estimation Using Weak Separability," Econometric Society World Congress 2000 Contributed Papers 1241, Econometric Society.

    More about this item

    Keywords

    Nonparametric regression; dimension reduction; kernel estimation; single-index model; partially linear model;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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