%0 Book Section %1 Groeneboom.Jongbloed2013 %A Groeneboom, Piet %A Jongbloed, Geurt %B From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner %C Beachwood, Ohio, USA %D 2013 %I Institute of Mathematical Statistics %K boundaryEffects hazardRate smoothing %P 174--196 %R 10.1214/12-IMSCOLL913 %T Smooth and non-smooth estimates of a monotone hazard %U http://projecteuclid.org/euclid.imsc/1362751187 %X We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval $0,a$. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points $0$ and $a$. We use penalization to obtain uniformly consistent estimators. Moreover, we determine the optimal penalization constants, extending related work in this direction by Statist. Sinica 3 (1993) 501–515; Ann. Statist. 27 (1999) 338–360. Two methods of obtaining smooth monotone estimates based on a non-smooth monotone estimator are discussed. One is based on kernel smoothing, the other on penalization.

@incollection{Groeneboom.Jongbloed2013, abstract = {We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval $[0,a]$. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points $0$ and $a$. We use penalization to obtain uniformly consistent estimators. Moreover, we determine the optimal penalization constants, extending related work in this direction by [Statist. Sinica 3 (1993) 501–515; Ann. Statist. 27 (1999) 338–360]. Two methods of obtaining smooth monotone estimates based on a non-smooth monotone estimator are discussed. One is based on kernel smoothing, the other on penalization. }, added-at = {2014-04-01T12:25:51.000+0200}, address = {Beachwood, Ohio, USA}, author = {Groeneboom, Piet and Jongbloed, Geurt}, biburl = {https://www.bibsonomy.org/bibtex/2c5acedb5381616fc61a135c1d97a8f57/marsianus}, booktitle = { From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner}, doi = {10.1214/12-IMSCOLL913}, interhash = {f8449f99bc00f932d8aa46a132e0dad8}, intrahash = {c5acedb5381616fc61a135c1d97a8f57}, keywords = {boundaryEffects hazardRate smoothing}, pages = {174--196}, publisher = {Institute of Mathematical Statistics}, timestamp = {2014-04-01T12:25:51.000+0200}, title = {Smooth and non-smooth estimates of a monotone hazard}, url = {http://projecteuclid.org/euclid.imsc/1362751187}, year = 2013 }