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含测量误差的分位数回归AI 解读

We devise a novel estimator for a general quantile regression model with normal measurement errors in the covariates. The method is applicable to both linear and nonlinear quantile regressions and does not impose the quantile requirement on multiple quantile levels simultaneously. We circumvent the difficulties caused by discontinuity in quantile regression through kernel smoothing, and overcome the nonlinearity inherent in quantile regression via considering extension to…

二次测量稀疏回归的弱凸凹正则化：支撑恢复与 ℓ2 误差界AI 解读

The recovery of unknown signals from quadratic measurements finds extensive applications in fields such as phase retrieval, power system state estimation, and unlabeled distance geometry. This paper investigates the finite sample properties of weakly convex--concave regularized estimators in high-dimensional quadratic measurements models. By employing a weakly convex--concave penalized least squares approach, we establish support recovery and $\ell_2$-error bounds for the…