Nonparametric estimation of P(X<Y) using local linear methods for weakly dependent data

This study addresses the problem of accurately estimating P(X<Y), particularly in the presence of weakly dependent data. Traditional nonparametric methods often assume independence between observations, which can lead to biased results in dependent settings. To overcome this limitation, we propose the use of local linear methods for the nonparametric estimation of P(X<Y), focusing on weakly dependent data modeled using an autoregressive (AR(1)) process. The primary objective is to assess the performance of the local linear estimator under both independent and weakly dependent conditions, comparing bias, variance, and mean squared error (MSE). A Monte Carlo simulation with 1000 repetitions was conducted, utilizing large sample sizes to ensure robust asymptotic properties. Results show that while the estimator performs well for independent data, with low bias and variance, its accuracy decreases significantly in the presence of weak dependence, leading to increased prejudice and MSE. These findings highlight the need for adjustments in nonparametric methods when dealing with dependent data. In conclusion, while effective for independent cases, the local linear method demonstrates limitations when applied to weakly dependent data, emphasizing the importance of considering dependence structures in future nonparametric estimations.