کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10524699 957594 2005 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Rate optimal estimation with the integration method in the presence of many covariates
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
Rate optimal estimation with the integration method in the presence of many covariates
چکیده انگلیسی
For multivariate regressors, integrating the Nadaraya-Watson regression smoother produces estimators of the lower-dimensional marginal components that are asymptotically normally distributed, at the optimal rate of convergence. Some heuristics, based on consistency of the pilot estimator, suggested that the estimator would not converge at the optimal rate of convergence in the presence of more than four covariates. This paper shows first that marginal integration with its internally normalized counterpart leads to rate-optimal estimators of the marginal components. We introduce the necessary modifications and give central limit theorems. Then, it is shown that the method apply also to more general models, in particular we discuss feasible estimation of partial linear models. The proofs reveal that the pilot estimator shall over-smooth the variables to be integrated, and, that the resulting estimator is itself a lower-dimensional regression smoother. Hence, finite sample properties of the estimator are comparable to those of low-dimensional nonparametric regression. Further advantages when starting with the internally normalized pilot estimator are its computational attractiveness and better performance (compared to its classical counterpart) when the covatiates are correlated and nonuniformly distributed. Simulation studies underline the excellent performance in comparison with so far known methods.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 95, Issue 2, August 2005, Pages 246-272
نویسندگان
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