An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies

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11 Scopus citations


We present a novel nonparametric method for bioassay and benchmark analysis in risk assessment, which averages isotonic MLEs based on disjoint subgroups of dosages. The asymptotic theory for the methodology is derived, showing that the MISEs (mean integrated squared error) of the estimates of both the dose-response curve F and its inverse F-1 achieve the optimal rate O(N-4/5). Also, we compute the asymptotic distribution of the estimate ζ̃p of the effective dosage ζp=F-1(p) which is shown to have an optimally small asymptotic variance.

Original languageEnglish (US)
Pages (from-to)1947-1953
Number of pages7
JournalStatistics and Probability Letters
Issue number23-24
Publication statusPublished - Dec 2010



  • Asymptotic normality
  • Benchmark analysis
  • Effective dosage
  • Mean integrated square error
  • Monotone dose-response curve estimation

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

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