ABSTRACT The focus of the present paper is on the uniform in bandwidth consistency of kernel-type estimators of the regression function derived by modern empirical process theory, under weaker conditions on the kernel than previously used in the literature. Our theorems allow data-driven local bandwidths for these statistics. We extend existing uniform bounds on kernel regression estimator and making it adaptive to the intrinsic dimension of the underlying distribution of which will be characterising by the so-called intrinsic dimension. Moreover, we show, in the same context, the uniform in bandwidth consistency for nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. Statistical applications to the kernel-type estimators (density, regression, conditional distribution, derivative functions, entropy, mode and additive models) are given to motivate these results.

中文翻译：

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在存在删失数据的情况下，内核回归估计器的均匀收敛率适应于内在维度

摘要 本文的重点是在内核上比以前在文献中使用的条件更弱的情况下，由现代经验过程理论推导出的回归函数的内核类型估计量在带宽一致性上的一致性。我们的定理允许数据驱动的本地带宽用于这些统计数据。我们扩展了核回归估计量的现有统一边界，使其适应潜在分布的内在维度，其特征是所谓的内在维度。此外，我们在相同的上下文中展示了随机审查下回归函数的审查加权 (IPCW) 估计量的非参数逆概率的带宽一致性的一致性。核型估计器的统计应用（密度、回归、条件分布、