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.

中文翻译：

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基于NA和有偏样本的带变点密度函数的逐点小波估计

本文关注的是存在多个变化点的负相关偏置样本的密度估计问题。我们使用峰值超过阈值方法来估计变化点的数量和位置，并给出等距设计估计来评估基础密度函数的跳跃大小。随后，我们提出了潜在密度的非线性小波变点估计，并显示了 Besov 空间上逐点风险下的收敛速度。需要指出的是，小波变点估计的收敛速度接近最优（达到对数项），并且与没有变点的普通小波密度估计保持一致。