In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process. In practice, however, the processes are typically only observed at discrete points and one has to resort to interpolation to fill in the gaps. We discuss the influence of such an interpolation on estimators of marginal parameters as well as estimators of the exponent measure. In particular, natural conditions on the fineness of the observational scheme are developed which ensure that asymptotically the interpolated estimators behave in the same way as the estimators which use fully observed continuous processes.

Additional Metadata
Keywords Discrete and continuous sampling, Interpolation, Max-stable process, Primary—62G32, Secondary—62G05, 62M30
Persistent URL dx.doi.org/10.1007/s10687-018-0313-0, hdl.handle.net/1765/112151
Journal Extremes: statistical theory and applications in science, engineering and economics
Citation
Drees, H, de Haan, L.F.M, & Turkman, F. (Feridun). (2018). Extreme value estimation for discretely sampled continuous processes. Extremes: statistical theory and applications in science, engineering and economics, 21(4), 533–550. doi:10.1007/s10687-018-0313-0