演講者簡介 : Professor Chen received his Ph.D. in Economics from University College London in 2009. He is currently an Associate Research Fellow at the Institute of Economics, Academia Sinica. His research interests are Microeconometrics, Econometric theory, Applied econometrics, Statistics.
演講摘要 : We consider both L0-penalized and L0-constrained quantile regression estimators. For the L0-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and apply it to obtain non-asymptotic upper bounds on the mean-square parameter and regression function estimation errors. We also derive analogous results for the L0-constrained estimator. The resulting rates of convergence are nearly minimax-optimal and the same as those for L1-penalized estimators. Further, we characterize expected Hamming loss for the L0-penalized estimator. We implement the proposed procedure via mixed integer linear programming and also a more scalable first-order approximation algorithm. We illustrate the finite-sample performance of our approach in Monte Carlo experiments and its usefulness ina real data application concerning conformal prediction of infant birth weights. In sum, our L0-based method produces a much sparser estimator than the L1-penalized approach without compromising precision.
