Subvector Inference in Local Regression

• Activity Number: 616
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Ke-Li Xu*+
• Companies: Texas A&M University
• Keywords: Bayesian method ; empirical likelihood ; non-smooth criterion function ; nonparametric and semiparametric inference ; regression discontinuity

Abstract

We consider inference of nonparametric regression estimate when the dependent variable involves unknown quantities, which are also estimated in preliminary steps of local regressions. Motivated by two applications in local treatment effects and real-time predictive risk management, we aim to provide a general approach to inference that does not require case-by-case standard error calculation. Using the framework of estimating equations, we establish the sandwich form of the asymptotic variance, however, its estimator is not obvious when the estimating equations are not smooth in unknown quantities. We then propose using the empirical likelihood that leads to automatically pivotalized test statistics. To establish the chi-square limit, the key step is the plug-in estimation of the unknown quantities. We consider both the profiled estimator and the Laplace-type estimator. The second method has the Bayesian EL interpretation and is computationally attractive using the MCMC-algorithm. Simulations and an empirical application to testing local quantile treatment effects in the RD design are reported.