Deconvolution of ℙ(<italic>Xt</italic> < <italic>Yt</italic>) for stationary processes with supersmooth error distributions.

This paper focuses on nonparametrically estimating the probability $ \mathbb {P} \left ( X_t \lt Y_t \right ) $ P(Xt<Yt) when two strongly mixing stationary processes, $ X_t $ Xt and $ Y_t $ Yt, are observed with additional errors at discrete time points $ t_j = j\Delta $ tj=jΔ (where Δ is a positive constant). This problem has practical significance in some applications where data is time-dependent random variable sequences (generated from stochastic processes) like time-dependent stress–strength reliability modelling and receiver operating characteristic (ROC) curve analysis. We extend our analysis to account for errors generated from another strongly mixing stationary processes and derive convergence rate and asymptotic normality results for the estimator under supersmooth error distributions. Through applications and simulations, we illustrate the properties of our estimator. [ABSTRACT FROM AUTHOR]