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学者姓名：刘有明
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Abstract ：
Cai and Zhang (2018) established separate perturbation upper bound estimators for canonical correlation directions under centered Gaussian population and some conditions on the minimum singular value sigma(r)(S) of a correlation matrix S . They posed an open problem for the optimality of their estimators. In this paper, the optimality of Cai and Zhang's estimation is firstly proved up to some multiplicated constants. Then motivated by Ma and Li's work (Ma and Li, 2020), we give an upper bound estimation for centered sub-Gaussian population, and a better estimate for bounded sub-Gaussian population. Finally, all estimates are extended from centered population to non-centered one. (C) 2021 Elsevier Inc. All rights reserved.
Keyword ：
Singular value decomposition Singular value decomposition Canonical correlation directions Canonical correlation directions Gaussian and sub-Gaussian population Gaussian and sub-Gaussian population Optimal estimation Optimal estimation sine Theta distance sine Theta distance
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| GB/T 7714 | Liu, Youming , Ren, Chunguang . Estimation of canonical correlation directions: From Gaussian to sub-Gaussian population [J]. | JOURNAL OF MULTIVARIATE ANALYSIS , 2021 , 186 . |
| MLA | Liu, Youming 等. "Estimation of canonical correlation directions: From Gaussian to sub-Gaussian population" . | JOURNAL OF MULTIVARIATE ANALYSIS 186 (2021) . |
| APA | Liu, Youming , Ren, Chunguang . Estimation of canonical correlation directions: From Gaussian to sub-Gaussian population . | JOURNAL OF MULTIVARIATE ANALYSIS , 2021 , 186 . |
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Abstract ：
This current paper shows the asymptotic normality for wavelet deconvolution density estimators, when a density function belongs to some L-P(R) (p > 2) and the noises are moderately ill-posed with the index beta. The estimators include both the linear and non-linear wavelet ones. It turns out that the situation for 0 < beta <= 1 is more complicated than that for beta > 1. (C) 2018 Elsevier Inc. All rights reserved.
Keyword ：
Central limit theorem Central limit theorem Deconvolution Deconvolution Density function Density function Wavelet estimator Wavelet estimator
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| GB/T 7714 | Liu, Youming , Zeng, Xiaochen . Asymptotic normality for wavelet deconvolution density estimators [J]. | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS , 2020 , 48 (1) : 321-342 . |
| MLA | Liu, Youming 等. "Asymptotic normality for wavelet deconvolution density estimators" . | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 48 . 1 (2020) : 321-342 . |
| APA | Liu, Youming , Zeng, Xiaochen . Asymptotic normality for wavelet deconvolution density estimators . | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS , 2020 , 48 (1) , 321-342 . |
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Abstract ：
The perfect achievements have been made for L-P (1 <= p < +infinity) risk estimation, when a density function has compact support. However, there does not exist L-1 risk estimation for uncompactly supported densities in general. Motivated by the work of Juditsky & Lambert-Lacroix (A. Juditsky and S. Lambert-Lacroix, On minimax density estimation on R, Bernoulli, 10(2004), 187-220) and Goldenshluger & Lepski (A. Goldenshluger and O. Lepski, On adaptive minimax density estimation on R-d, Probab. Theory Relat. Fields., 159(2014), 479-543), we provide an adaptive estimate for a family of density functions not necessarily having compact supports in this paper.
Keyword ：
L-1 risk L-1 risk density function density function wavelets wavelets convergence rate convergence rate Besov space Besov space
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| GB/T 7714 | Cao, Kaikai , Liu, Youming . UNCOMPACTLY SUPPORTED DENSITY ESTIMATION WITH L-1 RISK [J]. | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS , 2020 , 19 (8) : 4007-4022 . |
| MLA | Cao, Kaikai 等. "UNCOMPACTLY SUPPORTED DENSITY ESTIMATION WITH L-1 RISK" . | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 19 . 8 (2020) : 4007-4022 . |
| APA | Cao, Kaikai , Liu, Youming . UNCOMPACTLY SUPPORTED DENSITY ESTIMATION WITH L-1 RISK . | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS , 2020 , 19 (8) , 4007-4022 . |
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Abstract ：
By using a kernel method, Lepski and Willer establish adaptive and optimal L-p risk estimations in the convolution structure density model in 2017 and 2019. They assume their density functions to be in a Nikol'skii space. Motivated by their work, we first use a linear wavelet estimator to obtain a point-wise optimal estimation in the same model. We allow our densities to be in a local and anisotropic Holder space. Then a data driven method is used to obtain an adaptive and near-optimal estimation. Finally, we show the logarithmic factor necessary to get the adaptivity.
Keyword ：
Anisotropic Holder space Anisotropic Holder space Optimality Optimality Point-wise risk Point-wise risk Wavelet Wavelet Density estimation Density estimation Adaptivity Adaptivity Generalized deconvolution model Generalized deconvolution model
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| GB/T 7714 | Liu, Youming , Wu, Cong . Point-Wise Wavelet Estimation in the Convolution Structure Density Model [J]. | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS , 2020 , 26 (6) . |
| MLA | Liu, Youming 等. "Point-Wise Wavelet Estimation in the Convolution Structure Density Model" . | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 26 . 6 (2020) . |
| APA | Liu, Youming , Wu, Cong . Point-Wise Wavelet Estimation in the Convolution Structure Density Model . | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS , 2020 , 26 (6) . |
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Abstract ：
Fan, Wang, and Zhong estimate the difference between the singular vectors of a matrix and those of a perturbed matrix in terms of the maximum norm. Their estimations are used effectively to establish the asymptotic properties of robust covariance estimators (see Journal ofMachine Learning Research, 2018;18:1-42). In this paper, we give the corresponding lower bound estimates, which show Fan-Wang-Zhong's estimations optimal.
Keyword ：
matrix perturbations matrix perturbations singular vector estimation singular vector estimation optimality optimality matrix norm matrix norm singular value decomposition singular value decomposition
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| GB/T 7714 | Liu, Youming , Qi, Xinyu . Optimality of singular vector perturbation under maximum norm [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2020 , 43 (8) : 5010-5018 . |
| MLA | Liu, Youming 等. "Optimality of singular vector perturbation under maximum norm" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 43 . 8 (2020) : 5010-5018 . |
| APA | Liu, Youming , Qi, Xinyu . Optimality of singular vector perturbation under maximum norm . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2020 , 43 (8) , 5010-5018 . |
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Abstract ：
Cai and Zhang establish separate perturbation bounds for sin Theta distances with spectral and Frobenius norms (Cai T, Zhang A. Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60-89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.
Keyword ：
optimality optimality norms of matrices norms of matrices perturbation bounds perturbation bounds projection matrix projection matrix singular values singular values
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| GB/T 7714 | Liu, Youming , Ren, Chunguang . An optimal perturbation bound [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2019 , 42 (11) : 3791-3798 . |
| MLA | Liu, Youming 等. "An optimal perturbation bound" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 42 . 11 (2019) : 3791-3798 . |
| APA | Liu, Youming , Ren, Chunguang . An optimal perturbation bound . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2019 , 42 (11) , 3791-3798 . |
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Abstract ：
This paper considers point-wise estimation of density functions under the local anisotropic Holder condition by the wavelet method. A linear wavelet estimate is first introduced and shown to be optimal. A data driven version is provided for adaptivity and the influence of the dimension is reduced under the independence structure of the estimated density. (C) 2018 Elsevier Inc. All rights reserved.
Keyword ：
Anisotropic density Anisotropic density Local Holder condition Local Holder condition Optimality Optimality Point-wise estimation Point-wise estimation Adaptivity Adaptivity
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| GB/T 7714 | Liu, Youming , Wu, Cong . Point-wise estimation for anisotropic densities [J]. | JOURNAL OF MULTIVARIATE ANALYSIS , 2019 , 171 : 112-125 . |
| MLA | Liu, Youming 等. "Point-wise estimation for anisotropic densities" . | JOURNAL OF MULTIVARIATE ANALYSIS 171 (2019) : 112-125 . |
| APA | Liu, Youming , Wu, Cong . Point-wise estimation for anisotropic densities . | JOURNAL OF MULTIVARIATE ANALYSIS , 2019 , 171 , 112-125 . |
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Abstract ：
This paper studies multivariate wavelet regression estimators with errors-in-variables under strong mixing data. We firstly prove the strong consistency for non-oscillating and Fourier-oscillating noises. Then, a convergence rate is provided for non-oscillating noises, when an estimated function has some smoothness. Finally, the consistency and convergence rate are discussed for a practical wavelet estimator.
Keyword ：
Practical estimator Practical estimator Errors-in-variables Errors-in-variables Regression estimation Regression estimation Wavelets Wavelets Strong mixing Strong mixing
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| GB/T 7714 | Guo, Huijun , Liu, Youming . Regression estimation under strong mixing data [J]. | ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS , 2019 , 71 (3) : 553-576 . |
| MLA | Guo, Huijun 等. "Regression estimation under strong mixing data" . | ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 71 . 3 (2019) : 553-576 . |
| APA | Guo, Huijun , Liu, Youming . Regression estimation under strong mixing data . | ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS , 2019 , 71 (3) , 553-576 . |
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Abstract ：
Using compactly supported wavelets, Gine and Nickl [Uniform limit theorems for wavelet density estimators, Ann. Probab. 37(4) (2009) 1605-1646] obtain the optimal strong L-infinity(R) convergence rates of wavelet estimators for a fixed noise-free density function. They also study the same problem by spline wavelets [Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections, Bernoulli 16(4) (2010) 1137-1163]. This paper considers the strong L-p(R) (1 <= p <= infinity) convergence of wavelet deconvolution density estimators. We first show the strong L-p consistency of our wavelet estimator, when the Fourier transform of the noise density has no zeros. Then strong L-p convergence rates are provided, when the noises are severely and moderately ill-posed. In particular, for moderately ill-posed noises and p = infinity, our convergence rate is close to Gine and Nickl's.
Keyword ：
Wavelets Wavelets additive noise additive noise strong convergence strong convergence bounded difference inequality bounded difference inequality density estimation density estimation
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| GB/T 7714 | Liu, Youming , Zeng, Xiaochen . Strong L-p convergence of wavelet deconvolution density estimators [J]. | ANALYSIS AND APPLICATIONS , 2018 , 16 (2) : 183-208 . |
| MLA | Liu, Youming 等. "Strong L-p convergence of wavelet deconvolution density estimators" . | ANALYSIS AND APPLICATIONS 16 . 2 (2018) : 183-208 . |
| APA | Liu, Youming , Zeng, Xiaochen . Strong L-p convergence of wavelet deconvolution density estimators . | ANALYSIS AND APPLICATIONS , 2018 , 16 (2) , 183-208 . |
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Abstract ：
Using a wavelet basis, we establish in this paper upper bounds of wavelet estimation on L p(Rd) risk of regression functions with strong mixing data for 1 <= p < infinity. In contrast to the independent case, these upper bounds have different analytic formulae for p. [1, 2] and p. (2,+infinity). For p = 2, it turns out that our result reduces to a theorem of Chaubey et al. (J Nonparametr Stat 25: 53-71, 2013); and for d = 1 and p = 2, it becomes the corresponding theorem of Chaubey and Shirazi (Commun Stat Theory Methods 44: 885-899, 2015).
Keyword ：
Strong mixing Strong mixing L p risk L p risk Wavelet Wavelet Regression estimation Regression estimation Convergence rate Convergence rate
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| GB/T 7714 | Kou, Junke , Liu, Youming . Wavelet regression estimations with strong mixing data [J]. | STATISTICAL METHODS AND APPLICATIONS , 2018 , 27 (4) : 667-688 . |
| MLA | Kou, Junke 等. "Wavelet regression estimations with strong mixing data" . | STATISTICAL METHODS AND APPLICATIONS 27 . 4 (2018) : 667-688 . |
| APA | Kou, Junke , Liu, Youming . Wavelet regression estimations with strong mixing data . | STATISTICAL METHODS AND APPLICATIONS , 2018 , 27 (4) , 667-688 . |
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