  The extremal index $\theta$, a measure of the degree of local dependence in
the extremes of a stationary process, plays an important role in extreme value
analyses. We estimate $\theta$ semiparametrically, using the relationship
between the distribution of block maxima and the marginal distribution of a
process to define a semiparametric model. We show that these semiparametric
estimators are simpler and substantially more efficient than their parametric
counterparts. We seek to improve efficiency further using maxima over sliding
blocks. A simulation study shows that the semiparametric estimators are
competitive with the leading estimators. An application to sea-surge heights
combines inferences about $\theta$ with a standard extreme value analysis of
block maxima to estimate marginal quantiles.
