Rank tests for independence for bivariate censored data (Q1079308)

Subject to study are the nonnegative bivariate i.i.d. random variables \(X_ n=(X_{1,n},X_{2,n})\), \(n=1,...,N\), which are interpreted as lifetimes of twins, married couples, etc. For each n, the censored variables \(Y_{i,n}=\min (Z_{i,n},X_{i,n})\), \(i=1,2\), are observed, where \((Z_{1,n},Z_{2,n})\), \(n=1,...,N\) are also i.i.d. Various rank statistics for testing the independence between \(X_{1,n}\) and \(X_{2,n}\) are studied. Theorems for asymptotical normality are proved.