In this work,we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods.The data are functional,independent and identically distributed,and are linked to a sin...In this work,we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods.The data are functional,independent and identically distributed,and are linked to a single-index model.Under general conditions,we establish the pointwise and uniform almost complete convergence,as well as the asymptotic normality of the estimator.We explicitly derive the asymptotic variance and,as a result,provide confidence bands for the theoretical parameter.A simulation study is conducted to illustrate the proposed methodology.展开更多
基金supported by PRFU of Ministry of Higher Education and Scientific Research Algeria(MESRS),University of Sciences and Technology Oran Mohamed Boudiaf(USTO-MB),Code:C00L03UN310220230005.
文摘In this work,we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods.The data are functional,independent and identically distributed,and are linked to a single-index model.Under general conditions,we establish the pointwise and uniform almost complete convergence,as well as the asymptotic normality of the estimator.We explicitly derive the asymptotic variance and,as a result,provide confidence bands for the theoretical parameter.A simulation study is conducted to illustrate the proposed methodology.
