Nonparametric estimation of splicing points in skewed cost distributions: a kernel-based approach

This paper proposes a nonparametric method for detecting splicing points within cost distributions. Leveraging techniques from change point detection, we adopt an asymmetric gamma kernel estimator to identify these transition points in often highly skewed distributions. Our method focuses on identifying locations within the distribution where a significant change occurs, allowing for the application of distinct models on either side of the splicing point. Theoretical properties of the estimator, including strong consistency and asymptotic normality, are established. In particular, it is demonstrated that the estimator is consistent with a faster convergence rate than the parametric one. Since this estimator tends to underestimate the splicing point in finite samples, we propose a bias correction method to enhance accuracy. Our proposed approach is validated through simulations and real data applications.