A statistical model to analyze different time scales of the variability of extreme high sea levels is presented. This model uses a time-dependent generalized extreme value (GEV) distribution to fit monthly maxima series and is applied to a large historical tidal gauge record (San Francisco, California). The model allows the identification and estimation of the effects of several time scales—such as seasonality, interdecadal variability, and secular trends—in the location, scale, and shape parameters of the probability distribution of extreme sea levels. The inclusion of seasonal effects explains a large amount of data variability, thereby allowing a more efficient estimation of the processes involved. Significant correlation with the Southern Oscillation index and the nodal cycle, as well as an increase of about 20% for the secular variability of the scale parameter have been detected for the particular dataset analyzed. Results show that the model is adequate for a complete analysis of seasonal-to-interannual sea level extremes providing time-dependent quantiles and confidence intervals.

The likelihood principle is one of the most important concepts in Statistics. Among other things, it is used to obtain point estimators for the parameters of probability distributions of random variables by maximizing the likelihood function. The resulting maximum likelihood estimators usually have desirable properties such as consistency and efficiency. However, these estimators are often not robust as it is known that there is usually a trade-off between robustness and efficiency; the more robust an estimator is the less efficient it may be when the data come from a Gaussian distribution. In this paper we investigate how the estimators change when the likelihood function is replaced by a trimmed version of it. The idea here is to trim the likelihood function rather than directly trim the data. Because the likelihood is scalar-valued, it is always possible to order and trim univariate as well as multivariate observations according to their contributions to the likelihood function. The degree of trimming depends on some parameters to be specified by the analyst. We show how this trimmed likelihood principle produces many of the existing estimators (e.g., maximum likelihood, least squares, least trimmed squares, least median of squares, and minimum volume ellipsoid estimators) as special cases. Since the resulting estimators may be very robust, they can be used for example for outliers detection. In some cases the estimators can be obtained in closed form. In other cases they may require numerical solutions. In cases where the estimators cannot be obtained in closed forms, we provide several algorithms for computing the estimates. The method and the algorithms are illustrated by several examples of both discrete and continuous distributions. © 1997 Elsevier Science B.V.