9617206 Koenker Quantile regression is gradually evolving into a comprehensive approach to the statistical analysis of linear and nonlinear response models. Although the application of quantile regression in empirical economics has grown rapidly in recent years in part because of the many past contributions by this project's investigator, applications of quantile methods to large problems have been limited because the computational burden increases rapidly as the problem size grows. This project pursues two lines of research which preliminary work by the investigator suggests should yield dramatic improvements in this direction. One is the use of recently developed interior point methods for linear programming; the other is a form of preprocessing which can drastically reduce the effective dimension of most quantile regression problems. Together, these ideas, based on preliminary testing, appear capable of bringing the computational effort of quantile regression down to the level of the standard least squares approach for problems with sample sizes up to several million observations, and perhaps larger. This project will refine these new methods and extend them to nonparametric and nonlinear response models. The project also addresses the problem of the bewildering array of methods of inference based on discrete quantiles by developing a method that appears especially attractive for a wide variety of quantile regression inference problems including the construction of confidence intervals for individual quantile regression parameter estimates. Finally the project uses quantile methods for economic applications in time-series, duration, and multivariate analysis.
