Smooth nonparametric estimation under monotonicity constraints

Doctoral thesis (2019)

Authors

E. Musta Statistics - EEMCS
Research Group
Statistics (EEMCS) (TU Delft)
Copyright: © 2019 E. Musta
DOI: https://doi.org/10.4233/uuid:35430f5f-daa8-49df-999f-bf97addd51ab
Central limit theorem Isotonic estimation Kernel smoothing Nonparametric estimation Maximum likelihood estimation Grenander-type estimator Cox regression model Global errors Confidence intervals Testing monotonicity Weak convergence
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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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.