Wavelet change-point estimation for the density based on biased sample

Abstract The appearance of change-points in the biased density estimation process may worsen the estimation effectiveness. To evaluate the density more accurately, we first detect the change-points by the peaks-over-threshold method and subsequently provide the estimation of the jump sizes. On the basis of change-point and their jump size estimations, we further propose the wavelet change-point density estimation and this estimation is shown to achieve the optimal convergence rate in theory. Furthermore, we present some examples that the biased density functions contain change-point(s) and implement the corresponding simulations to show that our proposed method improves the effectiveness of biased density estimation. Finally, the wavelet change-point density estimation is applied to a real-life dataset.