Abstract

The consistency of classical local linear kernel estimators in nonparametric regression is proved under constraints on design elements (regressors) weaker than those known earlier. The obtained conditions are universal with respect to the stochastic nature of design, which may be both fixed regular and random and is not required to consist of independent or weakly dependent random variables. Sufficient conditions for pointwise and uniform consistency of classical local linear estimators are stated in terms of the asymptotic behavior of the number of design elements in certain neighborhoods of points in the domain of the regression function.

中文翻译：

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关于局部线性核估计器一致性的充分条件

摘要

非参数回归中经典局部线性核估计量的一致性是在比早期已知的设计元素（回归量）弱的约束下得到证明的。所获得的条件对于设计的随机性质而言是通用的，其可以是固定的规则的和随机的，并且不需要由独立或弱相关的随机变量组成。经典局部线性估计量的逐点一致性和均匀一致性的充分条件是根据回归函数域中某些点邻域中的设计元素数量的渐近行为来描述的。