Semi-parametric inference for copula models for truncated data

Takeshi Emura*, Wei-Jing Wang, Hui-Nien Hung

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We investigate the dependent relationship between two failure time variables that truncate each other. Chaieb, Rivest, and Abdous (2006) proposed a semiparametric model under the so-called "semi-survival" Archimedean-copula assumption and discussed estimation of the association parameter, the truncation probability, and the marginal functions. Here the same model assumption is adopted but different inference approaches are proposed. For estimating the association parameter, we extend the conditional likelihood approach (Clayton (1978)) and the two-by-two table approach (Wang (2003)) to dependent truncation data. We further show that the three estimators, including that proposed by Chaieb, Rivest, and Abdous (2006), differ in weights. The likelihood approach provides the formula for a good weight. Large sample properties of the proposed methods are established by applying the functional delta method, which can handle estimating functions that are not in the form of U-statistics. Analytic formulae for the asymptotic variance estimators are provided. Two competing methods are compared via simulations, and applied to the transfusion-related AIDS data.

Original languageEnglish
Pages (from-to)349-367
Number of pages19
JournalStatistica Sinica
Issue number1
StatePublished - 1 Jan 2011


  • Archimedean copula model
  • Conditional likelihood
  • Functional delta method
  • Kendall's tau
  • Truncation data
  • Two-by-two table


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