论文标题
随机抽样设计下本地固定随机字段的非参数回归
Nonparametric regression for locally stationary random fields under stochastic sampling design
论文作者
论文摘要
在这项研究中，我们为局部固定的随机场（LSRFS）$ \ {{{\ bf x} _ {{\ bf s}，a_ {n}}}}，a_ {n}}}：{\ bf s}} $ {在$ r_ {n} = [0，a_ {n}]^{d} \ subset \ mathbb {r}^{d} $中的不规则间隔位置。我们首先得出了一般内核估计量的均匀收敛速率，其次是模型平均功能的估计量的渐近正态性。此外，我们考虑添加模型，以避免估计量对协变量数量的收敛速率的依赖性产生的维数的诅咒。随后，我们得出了加性功能的估计值的均匀收敛速率和关节渐近态性。我们还介绍了大约$ m_ {n} $ - 依赖性RFS，以提供LSRF的示例。我们发现这些RF包括宽类莱维驱动的移动平均RF。
In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in $R_{n} =[0,A_{n}]^{d} \subset \mathbb{R}^{d}$. We first derive the uniform convergence rate of general kernel estimators, followed by the asymptotic normality of an estimator for the mean function of the model. Moreover, we consider additive models to avoid the curse of dimensionality arising from the dependence of the convergence rate of estimators on the number of covariates. Subsequently, we derive the uniform convergence rate and joint asymptotic normality of the estimators for additive functions. We also introduce approximately $m_{n}$-dependent RFs to provide examples of LSRFs. We find that these RFs include a wide class of Lévy-driven moving average RFs.
