Estimating the Probability P(Xt<Yt) for m- dependent Processes from Noisy Data with Mixtures of Normal Errors

Tóm tắt

This study proposes a nonparametric estimation method for computing the probability D=P(Xt<Yt)
, where Xt and Yt are two m−dependent stationary processes subject to noise generated from a mixture of two normal distributions. Observations are made at discrete time points t j = ∆, with ∆ being a positive constant. This method has high practical significance in fields that require handling time-dependent random processes, such as reliability assessment for systems involved in the relationship between applied pressure and capacity (stress-strength model), or in analyzing Receiver Operating Characteristic (ROC) curves. We explore how to address complex noise structures and present results on the convergence rate of the Mean Squared Error (MSE) as well as the asymptotic normality of the estimator. The effectiveness of the method is demonstrated
through detailed simulations and an application analysis using real data from Duchenne Muscular
Dystrophy (DMD), highlighting that simple noise assumptions based on normal distributions may
not be sufficient to accurately capture the complexity observed in real-world scenarios.