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Abstract:
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In a spatial regression context, structural differences in the mean compared to other locations in small neighborhoods, or over the entire range of values under investigation, are of interest in various fields. Spatial differences may occur due to natural causes, societal changes, due to various biological processes and others. It is then of interest to detect locations where such differences occur. In particular, an external threshold maybe used to identify regions where a kernel estimate of the regression function crosses the predefined threshold. In this talk, we address asymptotic theory in particular when the regression errors are an unknown transformation of a latent Gaussian random field with long-range dependence and discuss some algorithmic details, such as optimum bandwidth selection. Numerical examples are used for motivation and to illustrate the findings. This is joint collaboration with Gabrielle Moser and Fan Wu, research done at the Statistics Lab, WSL, Switzerland.
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