RECENT PROGRESS IN THE NONPARAMETRIC ESTIMATION OF MONOTONE CURVES -WITH APPLICATIONS TO BIOASSAY AND ENVIRONMENTAL RISK ASSESSMENT.
RECENT PROGRESS IN THE NONPARAMETRIC ESTIMATION OF MONOTONE CURVES -WITH APPLICATIONS TO BIOASSAY AND ENVIRONMENTAL RISK ASSESSMENT.
复制标题
单调曲线非参数估计的最新进展 - 及其在生物测定和环境风险评估中的应用。
DOI：
10.1016/j.csda.2013.01.023
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发表时间：
2013
影响因子：
1.8
通讯作者：
Lin,Lizhen
中科院分区：
文献类型：
--
作者：
Bhattacharya,Rabi;Lin,Lizhen
最近用于估计单调回归函数F及其逆F−1的三种非参数方法是(1)逆核方法dnp(Dette et al.，2005；Dette and Scheder，2010)，(2)单调样条法(Kong and Eubank(2006))和(3)数据自适应方法NAM(Bhattacharya and Lin，2010,2011)，根植于保序回归(Ayer et al.，1955；Bhattacharya and Kong，2007)。这三种算法都具有渐近最优错误率。在本文中，通过对实际数据的分析，使用来自不同感兴趣的模型的广泛模拟来比较它们的有限样本性能。设自变量x在N个观测值y中有m个不同的值。结果表明，如果m相对于N相对较小，则通常情况下，NAM的性能最好，而当m为O(N)时，DNP的性能优于其他方法，除非自变量x的值有实质性的聚类性。
Three recent nonparametric methodologies for estimating a monotone regression function F and its inverse F−1are (1) the inverse kernel method DNP (Dette et al., 2005; Dette and Scheder, 2010), (2) the monotone spline (Kong and Eubank (2006)) and (3) the data adaptive method NAM (Bhattacharya and Lin, 2010, 2011), with roots in isotonic regression (Ayer et al., 1955; Bhattacharya and Kong, 2007). All three have asymptotically optimal error rates. In this article their finite sample performances are compared using extensive simulation from diverse models of interest, and by analysis of real data. Let there be m distinct values of the independent variable x among N observations y. The results show that if m is relatively small compared to N then generally the NAM performs best, while the DNP outperforms the other methods when m is O(N) unless there is a substantial clustering of the values of the independent variable x.