Estimation Under Order Restrictions

  • Ziv Shkedy
  • Dhammika Amaratunga
  • Marc Aerts
Part of the Use R! book series (USE R)


Chapter 2 covers the basic setting on which we focus in the first part of this book, i.e., the one in which a response variable Y is expected to increase or decrease monotonically with respect to increasing levels of a predictor variable x which in biomedical applications is usually the dose or concentration of a drug. We assume that the mean response is given by
$$E(Y \vert x) = \mu (x),$$
where μ( ) is an unknown monotone function. In Chap. 2, we focus on the estimation problem under order restriction using isotonic regression.


Maximum Likelihood Estimate Design Point Final Number Order Restriction Graphical Interpretation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Center for Statistics (CenStat)Hasselt UniversityDiepenbeekBelgium
  2. 2.Biostatistics and ProgrammingJansenn Pharmaceutical Companies of Johnson & JohnsonRaritanUSA

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