Estimation of monotone bivariate quantile residual life

The bivariate quantile residual life function can play an important role in statistical reliability and survival analysis. In many situations assuming a decreasing form for it is recommended. Here, we propose a new non-parametric estimator of this measure under such restriction. It has been shown that the new estimator is consistent and, with proper normalization, weakly converges to a bivariate Gaussian process. A simulation study shows that the proposed estimator is an alternative to the unrestricted estimator when the bivariate quantile residual life is decreasing. Finally, the new estimators are applied to two real data sets.