Exploring Regression Structure Using Nonparametric Functional Estimation
作者:
AlexanderM. Samarov,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1993)
卷期:
Volume 88,
issue 423
页码: 836-847
ISSN:0162-1459
年代: 1993
DOI:10.1080/01621459.1993.10476348
出版商: Taylor & Francis Group
关键词: Kernel estimation;Model selection;Nonparametric functional estimation;Nonparametric regression
数据来源: Taylor
摘要:
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 ofn–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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