Local polynomial estimation of a discontinuity point in log-density or its derivatives

The kernel estimator of density was studied by Rosenblatt (1956) and Parzen (1962), followed by numerous subsequent studies.Most of these studies focus on cases where the density is continuous.Huh (2002) studied the phenomenon that when the density or its derivatives have a discontinuity point, the estimation accuracy of the kernel estimator decreases near the discontinuity point.Otsu, Xu, and Matsushita (2013) and Mynbaev, Martins-Filho, and Henderson (2022) developed methods for inferring discontinuities in density estimates when the location of the discontinuity is known.Loader (1996a) estimated the density using a local polynomial estimator based on a log-likelihood function weighted by a kernel function.Based on Loader's estimation method, this study aims to propose an approach for estimating a discontinuity in density or its derivatives.We will conduct numerical experiments on the proposed estimators using simulation studies.