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Smooth estimation of mean residual life under random censoring

Yogendra P. Chaubey and Arusharka Sen

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We propose here a smooth estimator of the mean residual life function based on randomly censored data. This is derived by smoothing the product-limit estimator using the Chaubey-Sen technique (Chaubey and Sen (1998)). The resulting estimator does not suffer from boundary bias as is the case with standard kernel smoothing. The asymptotic properties of the estimator are investigated. We establish strong uniform consistency and asymptotic normality. This complements the work of Chaubey and Sen (1999) which considered a similar estimation procedure in the case of complete data. It is seen that the properties are similar, though technically more difficult to prove, to those in the complete data case with appropriate modifications due to censoring.

Chapter information

N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 35-49

First available in Project Euclid: 1 April 2008

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Digital Object Identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62G07: Density estimation

asymptotics Hille’s theorem mean residual life random censoring smoothing survival function

Copyright © 2008, Institute of Mathematical Statistics


Chaubey, Yogendra P.; Sen, Arusharka. Smooth estimation of mean residual life under random censoring. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 35--49, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000031.

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