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Exploring Regression Structure Using Nonparametric Functional Estimation

Alexander M. Samarov
Journal of the American Statistical Association
Vol. 88, No. 423 (Sep., 1993), pp. 836-847
DOI: 10.2307/2290772
Stable URL: http://www.jstor.org/stable/2290772
Page Count: 12
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Exploring Regression Structure Using Nonparametric Functional Estimation
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Abstract

Average derivative functionals of regression are proposed for nonparametric model selection and diagnostics. The functionals are of the integral type, which under certain conditions allows their estimation at the usual parametric rate of n-1/2. We analyze asymptotic properties of the estimators of these functionals, based on kernel regression. These estimators can then be used for assessing the validity of various restrictions imposed on the form of regression. In particular, we show how they could be used to reduce the dimensionality of the model, assess the relative importance of predictors, measure the extent of nonlinearity and nonadditivity, and, under certain conditions, help identify projection directions in projection pursuit models and decide on the number of these directions.

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