Nonparametric testing for the specification of spatial trend functions

Rongmao Zhang, Ngai Hang Chan and Changxiong Chi

Journal of Multivariate Analysis, 2023, vol. 196, issue C

Abstract: Correct specification of a spatial trend constitutes an important topic in statistics because it facilitates spatial kriging and inference. This paper proposes a global integrated squared error (GISE) statistics between the nonparametric smoothing surface and the parametric hypothesized model to test for the goodness-of-fit of spatial trends. By virtue of the m-dependence approximation of a stationary random field, it is shown that under certain regularity conditions, the proposed GISE statistics has an asymptotic normal distribution. Further, a grid-based block bootstrap (GBBB) procedure is also proposed to deal with the complicated asymptotic variance involved in the limit distribution. Numerical studies are also presented to illustrate the performance of the proposed method.

Keywords: Goodness-of-fit; Grid-based block bootstrap; m-dependence approximation; Nonparametric smoothing; Spatial trends (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2023.105180

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