Inferences on the Association Parameter in Copula Models for Bivariate Survival Data

Shih, Joanna H.; Louis, Thomas A.

doi:10.2307/2533269

Cited by 561 publications

(454 citation statements)

References 24 publications

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“…However, other copulas can be considered [12,14,29,30]. To this end, checking the goodness of ÿt of copulas to bivariate survival data can be carried out by using the method proposed by Wang and Wells [31], and an adaptation of this method to our framework is a topic for future research.…”

Section: Resultsmentioning

confidence: 99%

“…To this end, checking the goodness of ÿt of copulas to bivariate survival data can be carried out by using the method proposed by Wang and Wells [31], and an adaptation of this method to our framework is a topic for future research. It is also worth noting that, while in this work we considered Weibull marginal distributions, it is possible to use other distributional assumptions, or even use a semi-parametric approach with unspecifed baseline hazard functions [14].…”

Section: Resultsmentioning

confidence: 99%

“…When the hazard functions are speciÿed, maximum likelihood estimates of the parameters for joint model (1) and (2) can be obtained [13]. Alternatively, the two-stage parametric procedure proposed by Shih and Louis [14] can be used, in which parameters of the marginal survival functions S T1 and S T2 are estimated ÿrst (assuming independence), and then Â 12 is estimated conditional on the estimated values of the marginal parameters. This one-parameter family is closely related to the Plackett family of bivariate distributions [15].…”

Section: Bivariate Plackett-dale Model For Survival Datamentioning

confidence: 99%

See 2 more Smart Citations

Pseudo‐likelihood estimation for a marginal multivariate survival model

Tibaldi

Molenberghs

Burzykowski

et al. 2004

Statistics in Medicine

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SUMMARYIn this paper, we propose a multivariate Plackett-Dale model for survival outcomes. A pseudo-likelihood method for the estimation of the parameters is proposed and these ideas are applied to two case studies. The modelling approach is similar in spirit but di erent from Parner's approach. The ÿrst study is in AIDS, where the overall survival time and di erent opportunistic infections in HIV-infected patients are studied. The second study is on adoption data where the association of the survival times within families is modelled, illustrating the use of the proposed methodology for the context of population genetics.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Bivariate Plackett-dale Model For Survival Datamentioning

confidence: 99%

See 1 more Smart Citation

Pseudo‐likelihood estimation for a marginal multivariate survival model

Tibaldi

Molenberghs

Burzykowski

et al. 2004

Statistics in Medicine

View full text Add to dashboard Cite

show abstract

“…Since the calibration method cannot be used to estimate more than bivariate Archimedean copula parameters, the Maximum Pseudo-Likelihood (MPL) estimation is utilized in this study. The MPL is estimated by using pseudo data rather than the empirical distribution that is employed in the Canonical Maximum Likelihood (CML) method (Shih and Louis, 1995;Genest et al, 1995).…”

Section: Copula Distributionmentioning

confidence: 99%

Multivariate CTE for copula distributions

Hong¹,

Kim²

2017

Journal of the Korean Data and Information Science Society

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The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

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“…the between-household association not exceeding the within-house association. Let φ denote the parameters which specify the S j s, the pseudolikelihood approach for inference about θ has been proposed (Bandeen-Roche & Liang, 1996;Shih & Louis, 1995) as convenient estimators of φ are typically available by, for example, maximizing the likelihood function with respect to φ assuming independence, i.e. fixing θ 1 and θ 2 at 1.…”

Section: ·4 Example 3: Frailty Survival Modelsmentioning

confidence: 99%

On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems

Chen

Liang

2010

Biometrika

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SUMMARYThis paper considers the asymptotic distribution of the likelihood ratio statistic T for testing a subset of parameter of interest θ, θ = (γ, η), H 0 : γ = γ 0 , based on the pseudolikelihood L(θ,φ), whereφ is a consistent estimator of φ, the nuisance parameter. We show that the asymptotic distribution of T under H 0 is a weighted sum of independent chi-squared variables. Some sufficient conditions are provided for the limiting distribution to be a chi-squared variable. When the true value of the parameter of interest, θ 0 , or the true value of the nuisance parameter, φ 0 , lies on the boundary of parameter space, the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix, or from a mixture of multivariate normal distributions. A variety of examples are provided for which the limiting distributions of T may be mixtures of chi-squared variables. We conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments.

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Inferences on the Association Parameter in Copula Models for Bivariate Survival Data

Cited by 561 publications

References 24 publications

Pseudo‐likelihood estimation for a marginal multivariate survival model

Pseudo‐likelihood estimation for a marginal multivariate survival model

Multivariate CTE for copula distributions

On the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems

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