An Adaptive Filtering Procedure for Estimating Regression Quantiles

Applications of reliability theory and some forms of chance-constrained programming need real-time, nonstationary estimates of regression quantiles to trigger preventive actions, thereby avoiding undesirable system states. We have designed the Quantile Estimation Procedure (QEP) for this purpose. QEP is a new adaptive filter that nonparametrica11y estimates time-varying parameters of multivariate regression quantiles. Results of Monte Carlo tests show that QEP provides accurate estimates for a range of stochastic processes. Falling within this range is the case study of this paper on monitoring compliance with short-term air quality standards.