9320555 Koenker Quantile regression is gradually developing into a comprehensive approach to the statistical analysis of linear and non-linear response models. By supplementing the exclusive focus of least- squares-based methods on the estimation of conditional mean functions, with a general technique for estimating conditional quantile functions, it has greatly expanded the flexibility of both parametric and non-parametric statistical methods. Research is proposed on methods of inference for quantile regression, nonparametric quantile regression and smoothing, and economic applications. The new applications of quantile regression include non-parametric demand analysis and related welfare economics, several applications to time-series analysis, extensions to errors-in-variables and more general multivariate settings, and applications to survival analysis and duration models. There is already a well-developed theory of asymptotic inference for quantile regression. However, when inference on discrete quantiles is desired, as is increasingly common in econometric applications, one is faced with a rather bewildering array of methods based on direct estimation of the asymptotic covariance matrix, an approach which involves estimation of the reciprocal of the error density at the quantile of interest, or some form of the bootstrap. Versions of both approaches are available in existing econometric packages. Recently, however, three alternative approaches to inference have emerged. All of the new approaches share the advantage that they circumvent the necessity to directly estimate error density. This project will compare systematically the available methods for constructing confidence intervals and for linear hypothesis testing.
