# UL Extremes Webinar

## Next session

### Extremes modelling of imputed missing data under a periodic control

Random missing data can constitute a problem when modelling rare events. Imputation is crucial in these situations and therefore models that describe different imputation functions enhance possible applications and enlarge the few known families of models which cover these situations. In this talk, we consider a family of models $\{𝑌_𝑛\}$, $𝑛≥1$, that can be associated to automatic systems which have a periodic control, in the sense that it is guaranteed that at instants multiple of $T$, $T ≥ 2$, no value is lost. Random missing values are here replaced by the biggest of the previous observations up to the one surely registered.

We characterize the extremal behaviour of $\{𝑌_𝑛\}$, $𝑛\geq1$, and obtain its extremal index expression. A consistent estimator for the model parameter is also proposed and its finite sample behaviour analysed.

Joint work with Helena Ferreira (UBI) and Maria da Graça Temido (UC).

Joint seminar CEMAT and CEAUL

The UL Extremes Webinar project aims at bringing together on a regular basis (about once a month) all those interested in Extreme Value Theory and Applications. It should be an opportunity to share and discuss most recent research advances in the field. Emphasis shall be given to work developed in Portugal or with major Portuguese contribution.