TY - JOUR
T1 - Recent progress in the nonparametric estimation of monotone curves - With applications to bioassay and environmental risk assessment
AU - Bhattacharya, Rabi
AU - Lin, Lizhen
N1 - Funding Information:
This research was supported by NIH grant R21-ES016791 and NSF grant DMS 1107053 .
PY - 2013
Y1 - 2013
N2 - Three recent nonparametric methodologies for estimating a monotone regression function F and its inverse F-1 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 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.
AB - Three recent nonparametric methodologies for estimating a monotone regression function F and its inverse F-1 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 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.
KW - Adaptive method
KW - Bioassay application
KW - Finite sample comparison
KW - Monotone curves estimation
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U2 - 10.1016/j.csda.2013.01.023
DO - 10.1016/j.csda.2013.01.023
M3 - Article
AN - SCOPUS:84875917637
SN - 0167-9473
VL - 63
SP - 63
EP - 80
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
ER -