It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data.To solve the problem of typical observations when th...It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data.To solve the problem of typical observations when the covariates of the nonparametric component are functional,the robust estimates for the regression parameter and regression operator are introduced.The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic.We use thek Nearest Neighbors procedure(kNN)to construct the kernel estimator of the proposed robust model.Under some regularity conditions,we state consistency results for kNN functional estimators,which are uniform in the number of neighbors(UINN).Furthermore,a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach.展开更多
Under quite mild conditions onk n . the strong consistency is proved for the nearest neighbor density, the nearest neighbor kernel regression and the modified nearest neighbor kernel regression of an a-mixing stationa...Under quite mild conditions onk n . the strong consistency is proved for the nearest neighbor density, the nearest neighbor kernel regression and the modified nearest neighbor kernel regression of an a-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is $\sum\limits_{j = 1}^\infty {j^{a - 1} a(j)^{1 - 1/v}< \infty (a > 1} $ , $v > 1) or \sum\limits_{j = 1}^\infty {j^{a - 1} a(j)< \infty (a > 1} )$ . which is simple and weak.展开更多
In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly...In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.展开更多
<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under so...<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under some mild conditions, it is shown that the estimators are uniformly strongly consistent for both randomly complete data and censored data.展开更多
文摘It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data.To solve the problem of typical observations when the covariates of the nonparametric component are functional,the robust estimates for the regression parameter and regression operator are introduced.The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic.We use thek Nearest Neighbors procedure(kNN)to construct the kernel estimator of the proposed robust model.Under some regularity conditions,we state consistency results for kNN functional estimators,which are uniform in the number of neighbors(UINN).Furthermore,a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach.
文摘Under quite mild conditions onk n . the strong consistency is proved for the nearest neighbor density, the nearest neighbor kernel regression and the modified nearest neighbor kernel regression of an a-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is $\sum\limits_{j = 1}^\infty {j^{a - 1} a(j)^{1 - 1/v}< \infty (a > 1} $ , $v > 1) or \sum\limits_{j = 1}^\infty {j^{a - 1} a(j)< \infty (a > 1} )$ . which is simple and weak.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671012,11871072,11701004 and 11701005)the Natural Science Foundation of Anhui Province(Grant No.1508085J06)+2 种基金the Key Projects for Academic Talent of Anhui Province(Grant No.gxbjZD2016005)the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province(Grant No.2017H123)the Research Teaching Model Curriculum of Anhui University(Grant No.xjyjkc1407)
文摘In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.
基金Project supported by the National Natural Science Foundation of China.
文摘<正> For a wide class of nonparametric regression functions, the nearest neighbor estimator is constructed, and the uniform measure of deviation from the estimator to the regression function is studied. Under some mild conditions, it is shown that the estimators are uniformly strongly consistent for both randomly complete data and censored data.
