Models for extreme values are usually based on detailed asymptotic argument,
for which strong ergodic assumptions such as stationarity, or prescribed perturbations from
stationarity, are required. In most applications of extreme value modelling such assumptions
are not satis® ed, but the type of departure from stationarity is either unknown or complex,
making asymptotic calculations unfeasible. This has led to various approaches in which
standard extreme value models are used as building blocks for conditional or local
behaviour of processes, with more general statistical techniques being used at the modelling
stage to handle the non-stationarity. This paper presents another approach in this direction
based on penalized likelihood. There are some advantages to this particular approach: the
method has a simple interpretation; computations for estimation are relatively straightforward
using standard algorithms; and a simple reinterpretation of the model enables
broader inferences, such as con® dence intervals, to be obtained usingMCMC methodology.
Methodological details together with applications to both athletics and environmental data
are given.
