Editorial for the special issue on quantile regression and semiparametric methods

Quantile regression and other semiparametric models have been widely recognized as important data analysis tools in statistics and econometrics. Thesemethods donot rely strictly onparametric likelihoodbut avoid the curse of dimensionality associated with many nonparametric models. The journal Computational Statistics and Data Analysis regularly publishes papers on these semiparametric methods, see e.g. Debruyne et al. (2008), Møller et al. (2008), Zou and Yuan (2008), Shen (2009), Wang et al. (2009), Jurečková et al. (2010), Thompson et al. (2010), Yue and Rue (2011), Zhou (2011) among many others. This special issue focuses on the modeling and computational aspects of quantile regression and other semiparametric methods for modern data, which often have large numbers of observations and/or variables. Consequently we are often faced with issues such as censoring, variable selection, robustness and computational complexity. Quantile regression, proposed by Koenker and Bassett (1978), is used to model the conditional distribution of a random variable given a set of covariates. From this conditional distribution, the trimmed mean can be defined which, in finance, corresponds to the conditional expected shortfall, known to be a coherent risk measure. Leorato et al. (2012) present a new class of asymptotically efficient estimators for this trimmed mean. To cope with censored data, Pang et al. (2012) develop a new inference procedure for censored quantile regression based on induced smoothing. Lin et al. (2012) propose a new algorithm to estimate the regression quantiles when the response variable is subject to double censoring. Bang and Jhun (2012) tackle the problem of the automatic selection of grouped variables in quantile regression. Variable selection in binary and tobit quantile regression is addressed by Ji et al. (2012) using a Bayesian framework. When several response variables are available, so called multiple-output regression quantiles can be considered. A fast algorithm for their computation is proposed in Paindavaine and Siman (2012), and also leads to the fast computation of halfspace location depth contours. Semiparametric additive regression is studied in Christmann and Hable (2012) by means of support vector machines. To illustrate their method, they model the rent prices of houses in Munich, based on the size of the house, the construction year and the type of residential area. Sobotka and Kneib (2012) approach a similar problem using expectile regression. Whereas quantile regression is obtained byminimising aweighted sumof absolute residuals, expectile regressionminimizes a weighted sum of squared residuals. Semiparametric partial linear regression is considered in Raheem et al. (2012). They propose shrinkage estimators where the nonparametric component is approximated by a B-spline basis function. We hope that this issue will stimulate further research in a number of challenging areas, such as semiparametric models with random effects, estimation of nearly extreme conditional quantiles, proper use of Bayesian methods in quantile regression and other semiparametric models, and quantile analysis for multivariate data. We want to thank all authors who have submitted their papers for possible publication to the special issue, as well as all referees for their criticism and constructive comments on the submitted manuscripts.