Print Email Facebook Twitter Smooth nonparametric estimation under monotonicity constraints Title Smooth nonparametric estimation under monotonicity constraints Author Musta, E. (TU Delft Statistics) Contributor Jongbloed, G. (promotor) Lopuhaä, H.P. (promotor) Degree granting institution Delft University of Technology Date 2019-04-03 Abstract 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. Subject Isotonic estimationKernel smoothingNonparametric estimationMaximum likelihood estimationGrenander-type estimatorCox regression modelglobal errorsconfidence intervalstesting monotonicitycentral limit theoremWeak convergence To reference this document use: https://doi.org/10.4233/uuid:35430f5f-daa8-49df-999f-bf97addd51ab ISBN 978-94-6384-012-5 Part of collection Institutional Repository Document type doctoral thesis Rights © 2019 E. Musta Files PDF Thesis_Eni_Musta.pdf 1.9 MB Close viewer /islandora/object/uuid:35430f5f-daa8-49df-999f-bf97addd51ab/datastream/OBJ/view