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Interval-grouped data are defined, in general, when the event of interest cannot be directly observed and it is only known to have been occurred within an interval. In this framework, a nonparametric kernel density estimator is proposed and studied. The approach is based on the classical Parzen–Rosenblatt estimator and on the generalisation of the binned kernel density estimator. The asymptotic bias and variance of the proposed estimator are derived under usual assumptions, and the effect of using non-equally spaced grouped data is analysed. Additionally, a plug-in bandwidth selector is proposed. Through a comprehensive simulation study, the behaviour of both the estimator and the plug-in bandwidth selector considering different scenarios of data grouping is shown. An application to real data confirms the simulation results, revealing the good performance of the estimator whenever data are not heavily grouped. [ABSTRACT FROM AUTHOR]

Abstract: Nonparametric techniques are frequently used in seismology studies to fit statistical models to earthquake data, as an alternative to classical parametric methods. In this paper, we apply nonparametric techniques to study some area-characteristic seismic hazard parameters (such as the mean return period or the expected number of earthquakes) in the northwest of the Iberian Peninsula, using a complete data catalog. Moreover, bootstrap techniques are used to develop simultaneous confidence bands for these functions. The previous nonparametric approaches are adapted to a spatial framework, obtaining maps of the probabilities of exceedance of the annual maximum magnitude in the zone of study. This procedure suitably describes the features of the area studied, being consistent with previous geological researches. [Copyright &y& Elsevier]