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Open AccessArticle

Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample

by Renyu Ye 1,2, Xinsheng Liu 1,* and Yuncai Yu 1
1
State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2
School of Mathematics and Computation Science, Anqing Normal University, Anqing 246133, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 176; https://doi.org/10.3390/math8020176
Received: 14 December 2019 / Revised: 27 January 2020 / Accepted: 28 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Probability, Statistics and their Applications )
This paper focuses on the density estimation problem that occurs when the sample is negatively associated and biased. We constructed a block thresholding wavelet estimator to recover the density function from the negatively associated biased sample. The pointwise optimality of this wavelet density estimation is shown as L p ( 1 p < ) risks over Besov space. To validate the effectiveness of the block thresholding wavelet method, we provide some examples and implement the numerical simulations. The results indicate that our block thresholding wavelet density estimator is superior in terms of the mean squared error (MSE) when comparing with the nonlinear wavelet density estimator.
Keywords: pointwise optimality; wavelet; negatively associated; biased sample; density estimation pointwise optimality; wavelet; negatively associated; biased sample; density estimation
MDPI and ACS Style

Ye, R.; Liu, X.; Yu, Y. Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample. Mathematics 2020, 8, 176.

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