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arXiv · 1512.07445

Smooth estimation of a monotone hazard and a monotone density under random censoring

Hendrik P. Lopuhaä·Eni Musta
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Abstract

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 (though we can go arbitrarily close to the right boundary).

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Hendrik P. Lopuhaä, Eni Musta. 2018-05-17. Smooth estimation of a monotone hazard and a monotone density under random censoring. https://arxiv.org/abs/1512.07445

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