Facultade de Fisioterapia

Estimation of a monotone percentile residual life function under random censorship

Franco Pereira, Alba; de Uña-Álvarez, Jacobo
Abstract:
In this paper, we introduce a new estimator of a percentile residual life function with censored data under a monotonicity constraint. Specifically, it is assumed that the percentile residual life is a decreasing function. This assumption is usefulwhen estimating the percentile residual life of units,which degenerate with age.We establish a law of the iterated logarithm for the proposed estimator, and its √ n-equivalence to the unrestricted estimator. The asymptotic normal distribution of the estimator and its strong approximation to a Gaussian process are also established.We investigate the finite sample performance of the monotone estimator in an extensive simulation study. Finally, data from a clinical trial in primary biliary cirrhosis of the liver are analyzed with the proposed methods. One of the conclusions of our work is that the restricted estimator may be much more efficient than the unrestricted one.
Year:
2013
Type of Publication:
Article
Keywords:
Aging notions; Censored data; Nonparametric estimation; Reliability; Survival analysis
Journal:
Biometrical Journal
Volume:
55
Pages:
52-67
Month:
January
DOI:
http://dx.doi.org/10.1002/bimj.201100199
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