Search

Based on the classical estimation method of moments, a new copula estimator was proposed for censored bivariate data. As theoretical results, general formulas were proved with analytical forms of the obtained estimators. Taking into account Lopez and Saint-Pierre’s(2012)[19], Gribkova and Lopez’s (2015)[10] results, the asymptotic normality of the empirical survival copula was established. The dependence structure between the bivariate survival times was modeled under the assumption that the underlying copula is Archimedean. Accounting for various censoring patterns (singly or doubly censored), a simulation study was performed enlighten the behavior of the procedure estimation method, shown the efficiency and robustness of the new estimator proposed. Publisher's Version

In this paper, we consider nonparametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large number of estimators of the distribution function, and therefore for a large number of bivariate censoring frameworks. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in $l^{\infty}([0,1]^2).$ We derive the uniform convergence rates of the copula density estimators deduced from our smooth copula estimators. Investigation on the practical behavior of our estimators is done through a simulation study and two real data applications, corresponding to different censoring settings. We use our nonparametric estimators to define a goodness-of-fit procedure for parametric copula models. A new bootstrap scheme is proposed to compute the critical values.

In this paper, we provide a nonparametric estimator of the distribution of bivariate censored lifetimes, in a model where the two censoring variables differ only through an additional observed variable. This situation is motivated by a particular application to insurance, where the supplementary variable corresponds to the age difference between two individuals. Asymptotic results for our estimator are provided. The new tools that we develop are used to perform goodness-of-fit tests for survival copula models. The practical performance is illustrated through simulations and a real data analysis.

In this paper, we provide a new nonparametric estimator of the joint distribution of two lifetimes under random right censoring and left truncation, which can be seen as a bivariate extension of the Kaplan-Meier estimator. We derive asymptotic results for this estimator, including uniform $n^{1/2}-$consistency, and develop a general methodology to study bivariate lifetime modelling, which is a critical issue in the study of pensions with a reversion condition. Application to goodness-of-fit for survival copula models is discussed. We show that the procedure that we use are consistent, and propose a bootstrap procedure based on our estimator to compute the critical values. All the new techniques that we propose are experimented on the Canadian data-set initially studied by Frees et al. (1996).

In this paper we study a class of M-estimators in a regression model under bivariate random censoring and provide a set of sufficient conditions that ensure asymptotic n 1 / 2 - convergence . The cornerstone of our approach is a new estimator of the joint distribution function of the censored lifetimes. A copula approach is used to modelize the dependence structure between the bivariate censoring times. The resulting estimators present the advantage of being easily computable. A simulation study enlighten the finite sample behavior of this technique.

Let (T1, T2) be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper, a semiparametric estimator of the bivariate distribution function of (T1, T2) and, more generally, of a functional E[$\phi$(T1,T2)] is proposed. We assume that the probability of censoring for T2 given the (possibly censored) gap times belongs to a parametric family of binary regression curves. We investigate the conditions under which the introduced estimator is consistent. We explore the finite sample behavior of the estimator and of its bootstrap standard error through simulations. The main conclusion of this paper is that the semiparametric estimator may be much more efficient than purely nonparametric methods. Real data illustration is included., Fundação para a Ciência e a Tecnologia (FCT)

When using data from individuals who are in the labour force to disentangle the empirical relevance of cohort, age and time effects for sickness absence, the inference may be biased, affected by sorting-out mechanisms. One reason is unobserved heterogeneity potentially affecting both health status and ability to work, which can bias inference because the individuals entering the data set are conditional on being in the labour force. Can this sample selection be adequately handled by attaching unobserved heterogeneity to non-structured fixed effects? In the paper we examine this issue and discuss the econometric setup for identifying from such data time effects in sickness absence. The inference and interpretation problem is caused, on the one hand, by the occurrence of time, cohort and age effects also in the labour market participation, on the other hand by correlation between unobserved heterogeneity in health status and in ability to work. We show that running panel data regressions, ordinary or logistic, of sickness absence data on certain covariates, when neglecting this sample selection, is likely to obscure the interpretation of the results, except in certain, not particularly realistic, cases. However, the fixed individual effects approach is more robust in this respect than an approach controlling for fixed cohort effects only.

The paper discusses statistics that can be used to test whether two failure times, say $X_1$ and $X_2$, are independent. The two variables are subject to right censoring so that what is observed is $Y_i = \min(X_i, Z_i)$ and $\delta_i = I(X_i = Y_i)$, where $(Z_1, Z_2)$ are censoring times independent of $(X_1, X_2)$. Statistics that generalize the Spearman rank correlation and the log-rank correlation are considered, as well as general linear rank statistics. The Chernoff-Savage approach is adopted to show that suitably standardized versions of these statistics are asymptotically normal under both fixed and converging alternatives.

In longitudinal studies of disease, patients can experience several events across a follow-up period. Analysis of such studies can be successfully performed by multistate models. This paper considers nonparametric and semiparametric estimation of important targets in multi-state modeling, such as the transition probabilities and bivariate distribution function (for sequentially ordered events). These estimators are shown to be consistent even for data which is non-Markov. We illustrate the methods on two data sets., Thanks to a referee for careful reading of the paper. Luis F. Meira-Machado acknowledges financial support by Grant PTDC/MAT/104879/2008 (FEDER support included) of the Portuguese Ministry of Science, Technology and Higher Education. The research was also partially funded by CMAT and FCT under the POCI 2010 program.