Title: Exact computation of censored least absolute deviations estimator
Authors: Yannis Bilias - Athens University of Economics and Business / RC (Greece) [presenting]
Abstract: Quantile Regression (QR) in the presence of censoring results in objective functions that need to be optimized which are non-convex and non-smooth. Approximate optimization algorithms proposed for the practitioners do not guarantee the finding of global optimizer. Under this scenario, the statistical properties of the QR estimator are not known and its use will lead to invalid inference. We propose the use of modern optimization methods for locating the global optimum in this class of estimation problems. We address the exact computation of Censored Least Absolute Deviations (CLAD) estimator by formulating the estimator as a linear Mixed Integer Programming (MIP) problem with disjunctive constraints. Application of our approach to previously studied datasets suggests that widely used approximate optimization algorithms can lead to erroneous conclusions. The exact computation of global optimum also allows us to compare the statistical properties of the Powell's estimator with those of other asymptotically equivalent competitors that are easier to compute.