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LOCAL POLYNOMIAL REGRESSION FOR SPATIAL DATA ON Rd

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  • Daisuke Kurisu
  • Yasumasa Matsuda

Abstract

In this study, we develop a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region Rn 竓 Rd. We adopt a stochastic sampling design that can generate irregularly spaced sampling sites in a flexible manner and include both pure increasing and mixed increasing domain framework. We first introduce a nonparametric regression model for spatial data defined on Rd and then establish the asymptotic normality of LP estimators with general order p >_ 1. We also propose methods for constructing confidence intervals and establish uniform convergence rates of LP estimators. Our dependence structure conditions on the underlying random field cover a wide class of random fields such as Levy-driven continuous autoregressive moving average random fields. As an application of our main results, we also discuss a two-sample testing problem for mean functions and their partial derivatives.

Suggested Citation

  • Daisuke Kurisu & Yasumasa Matsuda, 2022. "LOCAL POLYNOMIAL REGRESSION FOR SPATIAL DATA ON Rd," DSSR Discussion Papers 133, Graduate School of Economics and Management, Tohoku University.
    • Handle: RePEc:toh:dssraa:133
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    File URL: http://hdl.handle.net/10097/00136197
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