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An Invariance Principle for Discontinuity Estimation in Smooth Hazard Functions under Random Censoring

Hans-Georg Müller and Jane-Ling Wang
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 58, No. 3 (Oct., 1996), pp. 392-402
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25051118
Page Count: 11
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An Invariance Principle for Discontinuity Estimation in Smooth Hazard Functions under Random Censoring
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Abstract

Consider a hazard function which is smooth with the exception of a discontinuity or a discontinuity in its ν-th derivative. Nonparametric estimators for the discontinuity location are constructed by maximizing differences between left and right sided kernel estimates using smooth kernel functions. A local deviation process around the discontinuity location is introduced and an invariance principle is established. This result is applied to obtain asymptotic distributions of these estimators as well as corresponding estimators for the jump size. The methods and results are applicable to randomly censored data.

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