Edsel Peña
Department of Statistics
University of South Carolina
Estimation of an Event-Time Distribution
This talk pertains to the important statistical problem of
estimating a distribution function, in particular, the distribution of the
random variable pertaining to the occurrence of an event of interest such as
the failure of a machine, time to death, time to an insurance claim, etc.
First, given a simple random sample, we compare and contrast the resulting
parametric and nonparametric estimators, and consider the impact of model
misspecification. Second, we consider the situation where the event times
are right-censored, as is typical in biological, medical, public health,
engineering, and economic situations. For this setting, we present and
discuss the Kaplan-Meier or the product-limit estimator. Third, we consider
the situation where there are multiple event times per experimental unit
such as in the situation where the event is recurrent, and discuss
peculiarities and difficulties in this setting. Finally, we tackle the
setting where there are covariates, predictor, or marker variables. This
will entail a discussion of the popular Cox proportional hazards model. We
then describe a general model for recurrent events which simultaneously
takes into account several aspects in recurrent event modeling. For these
latter models we consider the problem of estimating a baseline distribution
function. The talk is meant to be an overview and will thus refrain from
delving deeply into mathematical technicalities.
Back to Colloquium Series