Inference on Multivariate M estimators based on bivariate censored data

Consider two random variables subject to random right censoring, for example, the survival times of twins or two recurrence times of a certain disease recorded on the same individual. Of interest is the estimation of a multivariate M functional of these two random variables. Asymptotic results for the proposed estimator are established under general conditions on the criterion function of the M estimator. The obtained results include the asymptotic normality of the estimator, its local power, and construction of a confidence region. Our primary example of interest is the bivariate L-1 median. We compare the small-sample behavior of this estimator with that of the vector of marginal medians by means of a simulation study. Finally, we consider a dataset on kidney dialysis patients and estimate the median time to two different infections for these individuals.