Nonparametric estimators of a regression function with circular response and R d -valued predictor are considered in this work. Local polynomial estimators are proposed and studied. Expressions for the asymptotic conditional bias and variance of these estimators are derived, and some guidelines to select asymptotically optimal local bandwidth matrices are also provided. The finite sample behavior of the proposed estimators is assessed through simulations and their performance is also illustrated with a real data set.
The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude and longitude are easy to fit and to interpret. However, the use of simple parametric models for characterizing spatially varying processes may lead to misspecification problems if the model is not appropriate. Recently, Meilán-Vila et al. ( 2019) proposed a goodness-offit test based on an L 2 -distance for assessing a parametric trend model with correlated errors, under random design, comparing a parametric and a nonparametric trend estimators. The present work aims to provide a detailed computational analysis of the behavior of this approach using different bootstrap algorithms for calibration, under a fixed-design geostatistical framework. Asymptotic results for the test are provided and an extensive simulation study, considering complexities that usually arise in geostatistics, is carried out to illustrate the performance of the proposal.
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