Smooth nonparametric estimation under monotonicity constraints

Eni Musta

Research output: ThesisDissertation (TU Delft)

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In this thesis we address the problem of estimating a curve of interest (which might be a probability density, a failure rate or a regression function) under monotonicity constraints. The main concern is investigating large sample distributional properties of smooth isotonic estimators, which have a faster rate of convergence and a nicer graphical representation compared to standard isotonic estimators such as the constrained nonparametric maximum likelihood and the Grenander-type estimator. In the first part, we focus on the pointwise behavior of estimators for the hazard rate in the right censoring and Cox regression models, while the second part is dedicated to global errors of estimators in a general setup, which includes estimation of a probability density, a failure rate, or a regression function. We provide central limit theorems and assess the finite sample performance of the estimators by means of simulation studies for constructing confidence intervals and goodness of fit tests.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Jongbloed, G., Supervisor
  • Lopuhaä, H.P., Supervisor
Award date3 Apr 2019
Electronic ISBNs978-94-6384-012-5
Publication statusPublished - 2019


  • Isotonic estimation
  • Kernel smoothing
  • Nonparametric estimation
  • Maximum likelihood estimation
  • Grenander-type estimator
  • Cox regression model
  • global errors
  • confidence intervals
  • testing monotonicity
  • central limit theorem
  • Weak convergence

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