Functional limits of empirical distributions in crossing theory |
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Authors: | Georg Lindgren |
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Institution: | Institute of Mathematical Statistics, University of Umea, S-901 87 Umea, Sweden |
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Abstract: | We present a functional limit theorem for the empirical level-crossing behaviour of a stationary Gaussian process. This leads to the well-known Slepian model process for a Gaussian process after an upcrossing of a prescribed level as a weak limit in C-space for an empirically defined finite set of functions.We also stress the importance of choosing a suitable topology by giving some natural examples of continuous and non-continuous functionals. |
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Keywords: | functional limit theorem empirical process stationary normal process level crossing |
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