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Smooth estimation of a monotone hazard and a monotone density under random censoring
Author(s) -
Lopuhaä Hendrik P.,
Musta Eni
Publication year - 2017
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12101
Subject(s) - mathematics , monotone polygon , estimator , censoring (clinical trials) , boundary (topology) , kernel (algebra) , smoothing , kernel density estimation , gaussian , consistency (knowledge bases) , kernel smoother , statistics , mathematical analysis , kernel method , combinatorics , discrete mathematics , computer science , physics , geometry , quantum mechanics , artificial intelligence , radial basis function kernel , support vector machine
We consider kernel smoothed Grenander‐type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n 2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).