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Recent progress in the nonparametric estimation of monotone curves—With applications to bioassay and environmental risk assessment

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  • Bhattacharya, Rabi
  • Lin, Lizhen

Abstract

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.

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  • Bhattacharya, Rabi & Lin, Lizhen, 2013. "Recent progress in the nonparametric estimation of monotone curves—With applications to bioassay and environmental risk assessment," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 63-80.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:63-80
    DOI: 10.1016/j.csda.2013.01.023
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    References listed on IDEAS

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    1. Dette, Holger & Neumeyer, Natalie & Pilz, Kay F., 2005. "A Note on Nonparametric Estimation of the Effective Dose in Quantal Bioassay," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 503-510, June.
    2. Bhattacharya, Rabi & Lin, Lizhen, 2010. "An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1947-1953, December.
    3. Lelys Bravo Guenni & Susan J. Simmons & Walter W. Piegorsch & Hui Xiong & Rabi N. Bhattacharya & Lizhen Lin, 2012. "Nonparametric estimation of benchmark doses in environmental risk assessment," Environmetrics, John Wiley & Sons, Ltd., vol. 23(8), pages 717-728, December.
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    Cited by:

    1. Lizhen Lin & Walter W. Piegorsch & Rabi Bhattacharya, 2015. "Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 713-731, September.
    2. Colubi, Ana & Domínguez-Menchero, J. Santos & González-Rodríguez, Gil, 2014. "Testing constancy in monotone response models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 45-56.

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