Monotone nonparametric regression with random design
Monotone nonparametric regression with random design
复制标题
随机设计的单调非参数回归
DOI：
10.3103/s1066530708040042
复制
发表时间：
2008
影响因子：
0.5
通讯作者：
C. Durot
中科院分区：
文献类型：
--
作者：
C. Durot
摘要本文研究了随机设计条件下回归函数的非参数最小二乘估计，该估计是单调的，即非递增的。在给定观测点的条件下，不假定误差是有条件的。特别是，这包括条件异方差的情况和当前状态模型的情况。$$
\mathbb{L}_p
$$ -误差显示为n - p/3阶，具有明确的渐近均值和方差的渐近高斯分布。
AbstractIn this paper we study the nonparametric least squares estimator of a regression function in a random design setting under the constraint that this function is monotone, say, nonincreasing. The errors are not assumed conditionally i.i.d. given the observation points. In particular, this includes the case of conditional heteroscedasticity and the case of the current status model. The $$
\mathbb{L}_p
$$-error is shown to be of order n−p/3 and asymptotically Gaussian with explicit asymptotic mean and variance.