On the identifiability of multivariate survival distribution functions (Q1102665)

Let \((T_ 1,T_ 2)\) be a non-negative random vector which is subjected to censoring random intervals \([X_ 1,Y_ 1]\) and \([X_ 2,Y_ 2]\). The censoring mechanism is such that the available informations on \(T_ 1\) and \(T_ 2\) are expressed by a pair of random vectors \(W=(W_ 1,W_ 2)\) and \(\delta =(\delta_ 1,\delta_ 2)\), where \(W_ i=\max (\min (Y_ i,T_ i),X_ i)\) and \[ \delta_ i = \begin{cases} 1,& \text{if \(X_ i\leq T_ i\leq Y_ i,\) \(i=1,2,\)} \\ 2,& \text{if \(T_ i>Y_ i,\) \(i=1,2,\)} \\ 3,& \text{if \(T_ i<X_ i,\) \(i=1,2\).} \end{cases} \] We will show that under some mild conditions the joint survival function of \(T_ 1\) and \(T_ 2\) can be expressed uniquely as functional of observable joint survival functions. Our results extend recent works on the randomly right censored bivariate data case and on the univariate problem with double censoring to the bivariate data with double censoring.