TY - JOUR

T1 - Semi-parametric inference for copula models for truncated data

AU - Emura, Takeshi

AU - Wang, Wei-Jing

AU - Hung, Hui-Nien

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - Archimedean copula model

KW - Conditional likelihood

KW - Functional delta method

KW - Kendall's tau

KW - Truncation data

KW - Two-by-two table

UR - http://www.scopus.com/inward/record.url?scp=78650385310&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:78650385310

VL - 21

SP - 349

EP - 367

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 1

ER -