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Exploring regression structure using nonparametric functional estimation. (English) Zbl 0790.62035
The author proposes functionals of average derivative type to explore the structure of a regression function. The estimation of these functionals is based on nonparametric kernel estimators. The estimators of these functionals are asymptotically normal, and it is shown, how they could be used to reduce the dimensionality of the regression model, to determine the relative importance of covariates, and to measure the extent of nonlinearity and nonadditivity of the model. Furthermore, under certain conditions these estimators are a useful tool in projection pursuit regression. The approach is illustrated by several simulation experiments and applications to real data sets.

MSC:
62G07Density estimation
62G05Nonparametric estimation
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