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

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Abstract

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.

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Acknowledgements

The authors would like to thank everyone for help. This work is supported by Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX\(19\_0149\)).

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  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, Jiangsu, People’s Republic of China

    Yuncai Yu

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  1. Yuncai Yu
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Yu, Y. Pointwise Wavelet Estimation of Density Function with Change-Points Based on NA and Biased Sample. Results Math 75, 146 (2020). https://doi.org/10.1007/s00025-020-01276-3

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