Nonparametric estimation of a distribution function from doubly truncated data under dependence

Carla Moreira (), Jacobo de Uña-Álvarez () and Roel Braekers ()
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Carla Moreira: University of Minho
Jacobo de Uña-Álvarez: SiDOR Research Group and CINBIO, University of Vigo
Roel Braekers: Hasselt University

Computational Statistics, 2021, vol. 36, issue 3, No 8, 1693-1720

Abstract: Abstract The NPMLE of a distribution function from doubly truncated data was introduced in the seminal paper of Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999). The consistency of the NPMLE depends however on the assumption of independent truncation. In this work we introduce an extension of the Efron–Petrosian NPMLE when the variable of interest and the truncation variables may be dependent. The proposed estimator is constructed on the basis of a copula function which represents the dependence structure between the variable of interest and the truncation variables. 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 two real data examples.

Keywords: Random double truncation; Copula function; Dependence; Interval sampling (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-021-01085-4

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