Estimation Under Order Restrictions

Chapter
Part of the Use R! book series (USE R)

Abstract

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.

Keywords

Maximum Likelihood Estimate Design Point Final Number Order Restriction Graphical Interpretation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Barlow, R. E., Bartholomew, D. J., Bremner, M. J., & Brunk, H. D. (1972). Statistical inference under order restriction. New York: Wiley.Google Scholar
  2. Cooke, R. M. (Ed.). (2009). Uncertainty modeling in dose-response. New York: Wiley.Google Scholar
  3. De Leeuw, J., Hornik, K., Mair, P. (2009). Isotone optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods. Journal of Statistical Software, 32(5), 1–24.Google Scholar
  4. Robertson, T., Wright, F. T., & Dykstra, R. L. (1988). Order restricted statistical inference. New York: Wiley.Google Scholar
  5. Silvapulle, M. J., & Sen, P. K. (2005). Constrained statistical inference: Order, inequality, and shape constraints. New York: Wiley.Google Scholar
  6. Hastie, T.J. and Tibshirani, R.J., (1990) Generalized Additive Models, Chapman & Hall/CRC.Google Scholar

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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