Pointwise Wavelet Estimation of Density Function with Change-Points Based on NA and Biased Sample

This paper is concerned with the density estimation problem of negatively associated biased sample with the presence of multiple change-points. We use the peaks-over-threshold approach to estimate the number and locations of change-points and give an equispaced design estimation to evaluate the jump sizes for the underlying density function. Subsequently, we propose a nonlinear wavelet change-point estimation of the underlying density and show the convergence rate under poinwise risk over Besov space. It should be pointed out that the convergence rate of wavelet change-point estimation is near optimal (up to a logarithmic term) and remains the same as that of the usual wavelet density estimation without change-points.