Nonparametric Estimation of a distribution function from doubly truncated data under dependence
release_upy5hiejcrdfzdsdaujss6bo4u
by
Carla Moreira, Jacobo de Uña-Álvarez, Roel Braekers
2021
Abstract
The NPMLE of a distribution function from doubly truncated data was
introduced in the seminal paper of Efron and Petrosian. The consistency of the
Efron-Petrosian estimator depends however on the assumption of independent
truncation. In this work we introduce an extension of the Efron-Petrosian NPMLE
when the lifetime and the truncation times may be dependent. The proposed
estimator is constructed on the basis of a copula function which represents the
dependence structure between the lifetime and the truncation times. Two
different iterative algorithms to compute the estimator in practice are
introduced, and their performance is explored through an intensive Monte Carlo
simulation study. We illustrate the use of the estimators on a real data
example.
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