Restoration of Monotonicity Respecting in Dynamic Regression
针对动态回归模型中标准估计方法无法保持单调性的问题，提出一种自适应插值方法，通过识别并插值原始估计量的最近单调性保持点来恢复单调性，且新估计量与原估计量渐近等价。
Dynamic regression models, including the quantile regression model and Aalen's additive hazards model, are widely adopted to investigate evolving covariate effects. Yet lack of monotonicity respecting with standard estimation procedures remains an outstanding issue. Advances have recently been made, but none provides a complete resolution. In this article, we propose a novel adaptive interpolation method to restore monotonicity respecting, by successively identifying and then interpolating nearest monotonicity-respecting points of an original estimator. Under mild regularity conditions, the resulting regression coefficient estimator is shown to be asymptotically equivalent to the original. Our numerical studies have demonstrated that the proposed estimator is much more smooth and may have better finite-sample efficiency than the original as well as, when available as only in special cases, other competing monotonicity-respecting estimators. Illustration with a clinical study is provided.