# Nonparametric regression for locally stationary random fields under stochastic sampling design

@article{Kurisu2020NonparametricRF, title={Nonparametric regression for locally stationary random fields under stochastic sampling design}, author={Daisuke Kurisu}, journal={arXiv: Statistics Theory}, year={2020} }

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… Expand

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