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学者姓名：刘有明
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Abstract ：
The misclassification rate can be used to measure the clustering accuracy. Cai and Zhang (2018) establish an upper bound of misclassification rate for the two-class clustering model Yi=mu l(i)+Zi is an element of R-p where li is an element of{-1,1} and Z(i)(i.i.d)similar to N(0,Ip),i is an element of{1,...,n},when the vector dimension p is larger than sample size n. The authors prove that their key assumption ||mu||(2)>= C-gap(p/n)(1/4) is necessary for any estimator to be consistent. This paper dis-cusses the same problem with sub-Gaussian noises and n >= p: We first use Cai and Zhang's method to give an upper bound of the misclassification rate for ||mu||(2)>= C-gap.Then a lower bound of the misclassification rate is provided under some technical conditions, which matches the upper bound up to a constant multiple. This shows our upper bound estimation optimal. Examples are given to explain those technical conditions easily satisfied. Similar to Cai and Zhang's work, we also prove the assumption ||mu||(2)>= C-gap in our upper bound estimation necessary for any estimator to be consistent as well. Finally, numerical simulations support our theoretical analysis.
Keyword ：
Misclassification rate Misclassification rate Sub-Gaussian noise Sub-Gaussian noise Clustering Clustering Statistical limit Statistical limit Optimality Optimality
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| GB/T 7714 | Liu, Youming , Zhang, Zhentao . Optimal estimation of misclassification rate for two-class clustering with sub-Gaussian noises [J]. | JOURNAL OF THE KOREAN STATISTICAL SOCIETY , 2024 . |
| MLA | Liu, Youming 等. "Optimal estimation of misclassification rate for two-class clustering with sub-Gaussian noises" . | JOURNAL OF THE KOREAN STATISTICAL SOCIETY (2024) . |
| APA | Liu, Youming , Zhang, Zhentao . Optimal estimation of misclassification rate for two-class clustering with sub-Gaussian noises . | JOURNAL OF THE KOREAN STATISTICAL SOCIETY , 2024 . |
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Abstract ：
Motivated by Jin-Ke-Wang's work (J. Jin, Z. T. Ke and W. Wang, Ann. Statist. 45(5) (2017) 2151-2189), this paper studies estimation of misclassification rate in the Asymptotic Rare and Weak (ARW) model. In contrast to Jin-Ke-Wang's theorem, we measure the performance of the estimator by the misclassification rate instead of Hamming distance, and extend the Gaussian noise to sub-Gaussian's. The probability estimation with convergence rate is first given under some conditions. Then we prove that condition necessary as well. A direct corollary of our estimation can be compared with Jin-Ke-Wang's theorem. It turns out that our statistical limit coincides with theirs.
Keyword ：
misclassification rate misclassification rate packing number packing number Kullback-Leibler divergence Kullback-Leibler divergence Clustering Clustering statistical limit statistical limit sub-Gaussian noise sub-Gaussian noise
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| GB/T 7714 | Liu, Youming , Zhang, Zhentao . Estimation of misclassification rate in the Asymptotic Rare and Weak model with sub-Gaussian noises [J]. | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2023 , 21 (04) . |
| MLA | Liu, Youming 等. "Estimation of misclassification rate in the Asymptotic Rare and Weak model with sub-Gaussian noises" . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 21 . 04 (2023) . |
| APA | Liu, Youming , Zhang, Zhentao . Estimation of misclassification rate in the Asymptotic Rare and Weak model with sub-Gaussian noises . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2023 , 21 (04) . |
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Abstract ：
Lower bound estimation plays an important role for establishing the minimax risk. A key step in lower bound estimation is deriving a lower bound of the affinity between two probability measures. This paper provides a simple method to estimate the affinity between mixture probability measures. Then we apply the lower bound of the affinity to establish the minimax lower bound for a family of sparse covariance matrices, which contains Cai-Ren-Zhou's theorem in [T. Cai, Z. Ren and H. Zhou, Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation, Electron. J. Stat. 10(1) (2016) 1-59] as a special example.
Keyword ：
Minimax risk Minimax risk Kullback-Leibler divergence Kullback-Leibler divergence lower bound estimation lower bound estimation sparse covariance matrix sparse covariance matrix affinity affinity mixture probability measure mixture probability measure
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| GB/T 7714 | Li, Huimin , Liu, Youming . Lower bound estimation for a family of high-dimensional sparse covariance matrices [J]. | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2023 , 22 (02) . |
| MLA | Li, Huimin 等. "Lower bound estimation for a family of high-dimensional sparse covariance matrices" . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 22 . 02 (2023) . |
| APA | Li, Huimin , Liu, Youming . Lower bound estimation for a family of high-dimensional sparse covariance matrices . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2023 , 22 (02) . |
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Abstract ：
As a technology of the green energy utilization, solar adsorption cooling is a promising way to make use of the solar energy in the future. Aiming to the efficiency improvement of such kind system, the performance of the solar adsorption cooling system that employed the silica gel-water as the working pair was evaluated experimentally. With a mono-axial solar collector of tracking parabolic trough to provide the heat supply to the adsorption bed, the effect of the adsorption time on the system performance was mainly addressed in the study. The experimental results revealed that the performance of the system reached the maximum as the adsorption time was 45 min. Correspondingly, the coefficient of performance of the system reached 0.258. In addition, a comparison of the optimal performance of the silica gel system to the SAPO-34 zeolite system was conducted. It was revealed that both the cooling capacity and the performance coefficient of the silica gel system depended more strongly on the adsorption time than those of the SAPO-34 zeolite system did. At the optimal adsorption time, the coefficient of performance of the silica gel system was 1.93 times as that of the SAPO-34 zeolite system. In general, the silica gel-water pair has shown better performance as compared to the SAPO-34 zeolite-water pair as used in the solar adsorption cooling system. © 2020 Elsevier Ltd
Keyword ：
Energy utilization Energy utilization Adsorption Adsorption Zeolites Zeolites Cooling Cooling Silica Silica Solar energy Solar energy Coefficient of performance Coefficient of performance Silica gel Silica gel Cooling systems Cooling systems Thermoelectric equipment Thermoelectric equipment
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| GB/T 7714 | Liu, Y.M. , Yuan, Z.X. , Wen, X. et al. Evaluation on performance of solar adsorption cooling of silica gel and SAPO-34 zeolite [J]. | Applied Thermal Engineering , 2021 , 182 . |
| MLA | Liu, Y.M. et al. "Evaluation on performance of solar adsorption cooling of silica gel and SAPO-34 zeolite" . | Applied Thermal Engineering 182 (2021) . |
| APA | Liu, Y.M. , Yuan, Z.X. , Wen, X. , Du, C.X. . Evaluation on performance of solar adsorption cooling of silica gel and SAPO-34 zeolite . | Applied Thermal Engineering , 2021 , 182 . |
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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 et al. "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 ：
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 et al. "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 ：
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 et al. "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 ：
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 et al. "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 ：
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 ：
Density function Density function Deconvolution Deconvolution Central limit theorem Central limit theorem 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 et al. "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 ：
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 et al. "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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