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B0320
Title: Quantile-regression inference with adaptive control of size Authors:  Juan Carlos Escanciano - Universidad Carlos III de Madrid (Spain) [presenting]
Abstract: Wald-type inference in the context of regression-quantile analysis generally requires the preliminary estimation of the conditional densities of the response variables at the quantile of interest. A new approach is developed to estimating the asymptotic variance of regression quantiles that leads the resulting Wald-type tests or confidence regions to behave as well in large samples as their infeasible counterparts in which the true conditional response densities are embedded. The new estimators of the regression quantile asymptotic variances are based on a new kernel-based approach to estimating the conditional response densities. Explicit guidance on implementing these density estimators is given, including a procedure for estimation of the optimal bandwidth from the point of view of adaptively controlling the size of any resulting Wald-type test. Monte Carlo evidence indicates the potential of our approach to deliver scalar confidence intervals for median regression parameters with excellent coverage accuracy. An empirical application is also included.