Pointwise wavelet change-points estimation for dependent biased sample

Abstract

This paper focuses on the multiple change-points detection for the biased regression function based on the dependent biased sample. A peaks-over-threshold method is utilized to detect the change-points and an equispaced design approach is provided to evaluate the jump sizes. On the basis of the change-points and jump sizes estimations, we propose a (Lp version of the) block thresholding estimator for the biased regression function. This block wavelet change-points estimator is adaptive and the optimal convergence rate of the proposed estimator is established on pointwise risk over Besov space with the presence of dependent bias. Additionally, the effectiveness of the proposed estimator is validated through some examples and numerical simulations.