Nonparametric estimation from censored data.
Abstract
For nearly two decades we have witnessed an intensive development
of a statistical methodology for assessing length of life and reliability
of performance from empirical data. The initial stimulus for
research on statistical problems in life testing and reliability came
from the need to answer pressing practical questions which could not be
treated by the existing statistical techniques. Because life and performance
tests are so time consuming and expensive to run, it is a practical necessity to terminate them as soon as possible. For the statistician this means developing estimation and decision
procedure for data, which are severely curtailed in one way or another
long before all items on test have actually failed. The estimation is
more complicated when the data are truncated, i.e. when the observer
loses track of some individuals before death occur. The product limit
method of Kaplan and Meier is one way of estimating p(t) when the
mechanism causing truncation is independent of the mechanism causing
death
.
This paper proposes alternative estimators and compares them to
the product limit method. A computer simulation is used to generate
the times of death and truncation from a variety of assumed distributions.
No single estimator gives the best fit to the "true" distribution
of death under all situations. However, other estimators are
shown to be better than the product limit estimator under all of the
assumed situations.
Description
Approved for public release; distribution is unlimited.
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