A0633
Title: Block maxima modelling in the presence of missing data
Authors: Emma Simpson - University College London (United Kingdom) [presenting]
Paul Northrop - University College London (United Kingdom)
Abstract: Modelling block maxima with the generalised extreme value (GEV) distribution is a common method for univariate extremes. One practical challenge in applying this methodology, which is often overlooked, is handling datasets containing missing values. In this case, one cannot be sure whether the true maximum has been observed in each block. If the issue is ignored, this can lead to biased GEV parameter estimates and subsequent underestimation of return levels, which is clearly undesirable when these are to be used for decision-making in practical applications. An approach that is often used to overcome this is to discard blocks where the proportion of missingness exceeds some specified threshold. This means that the chance of having recorded the maximum in each remaining block is reasonably high. While this is a sensible approach, extreme value modelling already comes with an intrinsic lack-of-data issue, so it would generally be preferable not to lose any of the information contained in these discarded blocks. An alternative approach is proposed, where the standard block maxima methodology is extended to overcome missing data issues. The proportion of missing values is explicitly accounted for in each block within the GEV model parameters. The inference is carried out using likelihood-based techniques, with return level estimates and confidence intervals obtained through profiling. The proposed methodology is demonstrated on environmental data.
