Pointwise Optimality of Wavelet Density Estimation for Negatively Associated Biased Sample

Renyu Ye, Xinsheng Liu and Yuncai Yu
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Renyu Ye: State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Xinsheng Liu: State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Yuncai Yu: State Key Laboratory of Mechanics and Control of Mechanical Structures, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Mathematics, 2020, vol. 8, issue 2, 1-12

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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