Monotone Regression Estimates for Grouped Observations
Monotone Regression Estimates for Grouped Observations
复制标题
分组观测的单调回归估计
DOI：
10.1214/aos/1176345710
复制
发表时间：
1982
影响因子：
4.5
通讯作者：
F. T. Wright
中科院分区：
文献类型：
--
作者：
F. T. Wright
具有正态分布误差的非递减回归函数的极大似然估计在文献中已被考虑。它在某一点的渐近分布与热方程解有关，其收敛到基本回归函数的速度为n-1/3阶。该估计器可以通过将相邻观测值分组，然后对相应的平均值进行“等序化”来修改。结果表明，对于一定的群体规模，所得到的估计量具有渐近正态分布，其收敛速度为n-215阶。给出了小样本量下的模拟研究结果，并讨论了分组过程。
The maximum likelihood estimator of a nondecreasing regression function with normally distributed errors has been considered in the literature. Its asymptotic distribution at a point is related to a solution of the heat equation, and its rate of convergence to the underlying regression function is of order n-1/3. This estimator can be modified by grouping adjacent observations and then "isotonizing" the corresponding means. It is shown that the resulting estimator has an asymptotic normal distribution for certain group sizes and its rate of convergence is of order n-215. The results of a simulation study for small sample sizes are presented and grouping procedures are discussed.