Bhattacharya Rabi, Lin Lizhen
The University of Arizona and Duke University.
Comput Stat Data Anal. 2013 Jul 1;63:63-80. doi: 10.1016/j.csda.2013.01.023.
Three recent nonparametric methodologies for estimating a monotone regression function and its inverse are (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 distinct values of the independent variable among observations . The results show that if is relatively small compared to then generally the NAM performs best, while the DNP outperforms the other methods when is () unless there is a substantial clustering of the values of the independent variable .
（1）逆核方法DNP（德特等人，2005年；德特和舍德，2010年）；（2）单调样条（孔和尤班克，2006年）；（3）数据自适应方法NAM（巴塔查里亚和林，2010年、2011年），其根源是保序回归（艾耶等人，1955年；巴塔查里亚和孔，2007年）。这三种方法都具有渐近最优误差率。在本文中，通过对各种感兴趣模型进行广泛模拟并分析实际数据，比较了它们的有限样本性能。假设有(n)个观测值，自变量有(k)个不同的值。结果表明，如果(k)相对于(n)较小，那么通常NAM表现最佳，而当(k)为（）时，除非自变量的值有大量聚类，DNP优于其他方法。
