An efficient semiparametric maxima estimator of the extremal index

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.Comment: 17 pages, 7 figures. Minor edits made to version 1 prior to journal publication. The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-015-0221-

A Selective Review of Group Selection in High-Dimensional Models

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group selection methods. In this article, we give a selective review of group selection concerning methodological developments, theoretical properties and computational algorithms. We pay particular attention to group selection methods involving concave penalties. We address both group selection and bi-level selection methods. We describe several applications of these methods in nonparametric additive models, semiparametric regression, seemingly unrelated regressions, genomic data analysis and genome wide association studies. We also highlight some issues that require further study.Comment: Published in at http://dx.doi.org/10.1214/12-STS392 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Brief history of the Lehmann Symposia: Origins, goals and motivation

The idea of the Lehmann Symposia as platforms to encourage a revival of interest in fundamental questions in theoretical statistics, while keeping in focus issues that arise in contemporary interdisciplinary cutting-edge scientific problems, developed during a conversation that I had with Victor Perez Abreu during one of my visits to Centro de Investigaci\'{o}n en Matem\'{a}ticas (CIMAT) in Guanajuato, Mexico. Our goal was and has been to showcase relevant theoretical work to encourage young researchers and students to engage in such work. The First Lehmann Symposium on Optimality took place in May of 2002 at Centro de Investigaci\'{o}n en Matem\'{a}ticas in Guanajuato, Mexico. A brief account of the Symposium has appeared in Vol. 44 of the Institute of Mathematical Statistics series of Lecture Notes and Monographs. The volume also contains several works presented during the First Lehmann Symposium. All papers were refereed. The program and a picture of the participants can be found on-line at the website http://www.stat.rice.edu/lehmann/lst-Lehmann.html.Comment: Published at http://dx.doi.org/10.1214/074921706000000347 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org