随机右删失数据下单调回归函数的估计

An Estimator of Monotone Regression Function With Randomly Right Censored Data

为了在随机右删失数据情况下,给出单调回归函数的合理估计,利用最大凸弱函数的理论和把未删失数据垫高的统计思想,得到了单调回归函数的一个新的估计.与核估计等传统的估计相比,该估计保证了单调性,因此在实际应用中(如儿童的生长曲线的制定等),当出现右删失情况且由历史经验或常识断定回归函数是单调函数时,该估计方法更加自然和贴近实际.并在一定的假设条件下,研究了该估计的渐近分布和相合性,得到了较好的极限性质.

The aim is to gain a rational estimator of monotone regression function with randomly right censored data.Using the theory of the greatest convex minorant and the statistical idea of padding the uncensored data highly,a new estimator is proposed.The estimator can guarantee monotone property,which is superior to traditional kernel estimators.Thus,in practical applications,such as establishing children's growth curve,when right censored data comes up and the regression function can be concluded to be monotone...