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学者姓名：熊贤祝
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Abstract ：
应用优函数罚方法求解具有低秩密度矩阵约束的最小二乘问题.首先，用凸差方法处理非凸的低秩约束，并结合罚方法和优函数方法将原问题转化为一系列具有密度矩阵约束的凸优化问题；然后，给出求解该优化问题的优函数罚方法，并对该方法进行收敛性分析；最后，运用半光滑牛顿增广拉格朗日算法求解优函数罚方法的子问题.合成数据集和真实数据集上的数值结果表明，优函数罚方法可有效求解具有低秩密度矩阵约束的最小二乘问题.
Keyword ：
优函数罚方法 优函数罚方法 低秩密度矩阵 低秩密度矩阵 最小二乘问题 最小二乘问题
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| GB/T 7714 | 罗曦 , 熊贤祝 , 刘勇进 . 求解低秩密度矩阵约束最小二乘问题的优函数罚方法 [J]. | 福州大学学报(自然科学版) , 2024 , 52 (02) : 127-133 . |
| MLA | 罗曦 等. "求解低秩密度矩阵约束最小二乘问题的优函数罚方法" . | 福州大学学报(自然科学版) 52 . 02 (2024) : 127-133 . |
| APA | 罗曦 , 熊贤祝 , 刘勇进 . 求解低秩密度矩阵约束最小二乘问题的优函数罚方法 . | 福州大学学报(自然科学版) , 2024 , 52 (02) , 127-133 . |
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Abstract ：
在应用众数回归方法来考虑非线性模型的估计时，把调整参数当作常数，在适当的条件下得到估计量的■收敛速度，改进了已有的众数回归估计方法，即把调整参数作为变量.最后，通过一定数量的模拟实验来验证众数回归估计的稳健性.
Keyword ：
众数回归方法 众数回归方法 ■收敛速度 ■收敛速度 调整参数 调整参数 非线性模型 非线性模型
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| GB/T 7714 | 张腾泽 , 熊贤祝 . 非线性模型的众数回归估计 [J]. | 福州大学学报(自然科学版) , 2024 , 52 (02) : 134-138 . |
| MLA | 张腾泽 等. "非线性模型的众数回归估计" . | 福州大学学报(自然科学版) 52 . 02 (2024) : 134-138 . |
| APA | 张腾泽 , 熊贤祝 . 非线性模型的众数回归估计 . | 福州大学学报(自然科学版) , 2024 , 52 (02) , 134-138 . |
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For a conditional density function (CDF) in the right-censored model, the local linear (LL) estimator has superior bias properties compared with the Nadaraya-Watson (NW) one, but it may have negative values and thus give rise to unsuitable inference. In order to alleviate the possible negativity of the LL estimator, we define a reweighted NW (RNW) estimator of the CDF in the right-censored model by employing the empirical likelihood (EL) method. The RNW estimator is constructed by modifying the NW estimator slightly, so it naturally inherits the nonnegativity of the NW one. It is assumed that the censoring time is independent of the survival time with the associated covariate. Under stationary alpha-mixing observations, the weak consistency and asymptotic normality of the RNW estimator are developed. The asymptotic normality shows that the RNW estimator possesses the bias and variance of the LL estimator. Finally, we conduct simulations to evaluate the finite sample performance of the estimator. (C) 2020 Elsevier B.V. All rights reserved.
Keyword ：
Asymptotic normality Asymptotic normality CDF CDF Nonnegativity Nonnegativity Right-censored model Right-censored model RNW estimator RNW estimator
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| GB/T 7714 | Xiong, Xianzhu , Ou, Meijuan , Chen, Ailian . Reweighted Nadaraya-Watson estimation of conditional density function in the right-censored model [J]. | STATISTICS & PROBABILITY LETTERS , 2021 , 168 . |
| MLA | Xiong, Xianzhu 等. "Reweighted Nadaraya-Watson estimation of conditional density function in the right-censored model" . | STATISTICS & PROBABILITY LETTERS 168 (2021) . |
| APA | Xiong, Xianzhu , Ou, Meijuan , Chen, Ailian . Reweighted Nadaraya-Watson estimation of conditional density function in the right-censored model . | STATISTICS & PROBABILITY LETTERS , 2021 , 168 . |
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This paper focuses on efficient algorithms for finding the Dantzig selector which was first proposed by Cande`\s and Tao as an effective variable selection technique in the linear regression. This paper first reformulates the Dantzig selector problem as an equivalent convex composite optimization problem and proposes a semismooth Newton augmented Lagrangian (SSNAL) algorithm to solve the equivalent form. This paper also applies a proximal point dual semismooth Newton (PPDSSN) algorithm to solve another equivalent form of the Dantzig selector problem. Comprehensive results on the global convergence and local asymptotic superlinear convergence of the SSNAL and PPDSSN algorithms are characterized under very mild conditions. The computational costs of a semismooth Newton algorithm for solving the subproblems involved in the SSNAL and PPDSSN algorithms can be cheap by fully exploiting the second order sparsity and employing efficient techniques. Numerical experiments on the Dantzig selector problem with synthetic and real data sets demonstrate that the SSNAL and PPDSSN algorithms substantially outperform the state-of-the-art first order algorithms even for the required low accuracy, and the proposed algorithms are able to solve the large-scale problems robustly and efficiently to a relatively high accuracy.
Keyword ：
augmented Lagrangian method augmented Lagrangian method Dantzig selector Dantzig selector proximal point method proximal point method semismooth Newton method semismooth Newton method
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| GB/T 7714 | Fang, Sheng , Liu, Yong-Jin , Xiong, Xianzhu . EFFICIENT SPARSE HESSIAN-BASED SEMISMOOTH NEWTON ALGORITHMS FOR DANTZIG SELECTOR\ast [J]. | SIAM JOURNAL ON SCIENTIFIC COMPUTING , 2021 , 43 (6) : A4147-A4171 . |
| MLA | Fang, Sheng 等. "EFFICIENT SPARSE HESSIAN-BASED SEMISMOOTH NEWTON ALGORITHMS FOR DANTZIG SELECTOR\ast" . | SIAM JOURNAL ON SCIENTIFIC COMPUTING 43 . 6 (2021) : A4147-A4171 . |
| APA | Fang, Sheng , Liu, Yong-Jin , Xiong, Xianzhu . EFFICIENT SPARSE HESSIAN-BASED SEMISMOOTH NEWTON ALGORITHMS FOR DANTZIG SELECTOR\ast . | SIAM JOURNAL ON SCIENTIFIC COMPUTING , 2021 , 43 (6) , A4147-A4171 . |
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In this paper, we study the local constant and the local linear estimators of the conditional density function with right-censored data which exhibit some type of dependence. It is assumed that the observations form a stationary mixing sequence. The asymptotic normality of the two estimators is established, which combined with the condition that implies the consistency of the two estimators and can be employed to construct confidence intervals for the conditional density function. The result on the local linear estimator of the conditional density function in Kim et al. (2010) is relaxed from the i.i.d. assumption to the mixing setting, and the result on the local linear estimator of the conditional density function in Spierdijk (2008) is relaxed from the rho-mixing assumption to the mixing setting. Finite sample behavior of the estimators is investigated by simulations.
Keyword ：
alpha-mixing alpha-mixing asymptotic normality asymptotic normality Conditional density function Conditional density function local constant and local linear estimators local constant and local linear estimators right-censored data right-censored data
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| GB/T 7714 | Xiong, Xianzhu , Ou, Meijuan . Non parametric estimation of the conditional density function with right-censored and dependent data [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2019 . |
| MLA | Xiong, Xianzhu 等. "Non parametric estimation of the conditional density function with right-censored and dependent data" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS (2019) . |
| APA | Xiong, Xianzhu , Ou, Meijuan . Non parametric estimation of the conditional density function with right-censored and dependent data . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2019 . |
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In this theoretical note, we revisit the problem of randomized sketches for kernel ridge regression in a reproducing kernel Hilbert space (RKHS). Under further smoothness conditions on the regression function, we show that the same sketching procedure automatically achieves faster rate which is minimax under such smoothness conditions. (C) 2019 Elsevier B.V. All rights reserved.
Keyword ：
Kernel method Kernel method Minimax rate Minimax rate Rademacher complexity Rademacher complexity Randomized sketches Randomized sketches
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| GB/T 7714 | Xiong, Xianzhu , Li, Rui , Lian, Heng . On nonparametric randomized sketches for kernels with further smoothness [J]. | STATISTICS & PROBABILITY LETTERS , 2019 , 153 : 139-142 . |
| MLA | Xiong, Xianzhu 等. "On nonparametric randomized sketches for kernels with further smoothness" . | STATISTICS & PROBABILITY LETTERS 153 (2019) : 139-142 . |
| APA | Xiong, Xianzhu , Li, Rui , Lian, Heng . On nonparametric randomized sketches for kernels with further smoothness . | STATISTICS & PROBABILITY LETTERS , 2019 , 153 , 139-142 . |
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In this article, we investigate the effect of surface tension in the Rayleigh-Taylor (RT) problem of stratified incompressible viscoelastic fluids. We prove that there exists an unstable solution to the linearized stratified RT problem with a largest growth rate Lambda under the instability condition (i.e., the surface tension coefficient v is less than a threshold v(c)). Moreover, for this instability condition, the largest growth rate Delta(v) decreases from a positive constant to 0, when v increases from 0 to v(c), which mathematically verifies that the internal surface tension can constrain the growth of the RT instability during the linear stage.
Keyword ：
Incompressible viscoelastic fluids Incompressible viscoelastic fluids Rayleigh-Taylor instability Rayleigh-Taylor instability Stratified fluids Stratified fluids Surface tension Surface tension
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| GB/T 7714 | Ma, Xingrui , Xiong, Xianzhu . On effect of surface tension in the Rayleigh-Taylor problem of stratified viscoelastic fluids [J]. | BOUNDARY VALUE PROBLEMS , 2019 , 2019 (1) . |
| MLA | Ma, Xingrui 等. "On effect of surface tension in the Rayleigh-Taylor problem of stratified viscoelastic fluids" . | BOUNDARY VALUE PROBLEMS 2019 . 1 (2019) . |
| APA | Ma, Xingrui , Xiong, Xianzhu . On effect of surface tension in the Rayleigh-Taylor problem of stratified viscoelastic fluids . | BOUNDARY VALUE PROBLEMS , 2019 , 2019 (1) . |
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This paper considers a nonparametric M-estimator of a regression function for functional stationary ergodic data. More precisely, in the ergodic data setting, we consider the regression of a real random variable Y over an explanatory random variable X taking values in some semi-metric abstract space. Under some mild conditions, the weak consistency and the asymptotic normality of the M-estimator are established. Furthermore, a simulated example is provided to examine the finite sample performance of the M-estimator.
Keyword ：
asymptotic normality asymptotic normality functional stationary ergodic data functional stationary ergodic data nonparametric M-estimator nonparametric M-estimator weak consistency weak consistency
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| GB/T 7714 | Xiong, Xian-zhu , Lin, Zheng-yan . Nonparametric M-estimation for Functional Stationary Ergodic Data [J]. | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2019 , 35 (3) : 491-512 . |
| MLA | Xiong, Xian-zhu 等. "Nonparametric M-estimation for Functional Stationary Ergodic Data" . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 35 . 3 (2019) : 491-512 . |
| APA | Xiong, Xian-zhu , Lin, Zheng-yan . Nonparametric M-estimation for Functional Stationary Ergodic Data . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2019 , 35 (3) , 491-512 . |
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This article focuses on the conditional density of a scalar response variable given a random variable taking values in a semimetric space. The local linear estimators of the conditional density and its derivative are considered. It is assumed that the observations form a stationary -mixing sequence. Under some regularity conditions, the joint asymptotic normality of the estimators of the conditional density and its derivative is established. The result confirms the prospect in Rachdi etal. (2014) and can be applied in time-series analysis to make predictions and build confidence intervals. The finite-sample behavior of the estimator is investigated by simulations as well.
Keyword ：
alpha-mixing dependence alpha-mixing dependence Conditional density Conditional density Functional data Functional data Joint asymptotic normality Joint asymptotic normality Local linear estimator Local linear estimator
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| GB/T 7714 | Xiong, Xianzhu , Zhou, Peiqin , Ailian, Chen . Asymptotic normality of the local linear estimation of the conditional density for functional time-series data [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2018 , 47 (14) : 3418-3440 . |
| MLA | Xiong, Xianzhu 等. "Asymptotic normality of the local linear estimation of the conditional density for functional time-series data" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 47 . 14 (2018) : 3418-3440 . |
| APA | Xiong, Xianzhu , Zhou, Peiqin , Ailian, Chen . Asymptotic normality of the local linear estimation of the conditional density for functional time-series data . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2018 , 47 (14) , 3418-3440 . |
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针对函数型数据下条件分位数的区间估计问题提出应用经验似然方法来构造条件分位数的置信区间,并在适当的条件下得到了经验似然比统计量渐近服从χ2(1).
Keyword ：
函数型数据 函数型数据 条件分位数 条件分位数 经验似然 经验似然 置信区间 置信区间
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| GB/T 7714 | 熊贤祝 , 周培钦 . 函数型数据下条件分位数的经验似然推断 [J]. | 福州大学学报（自然科学版） , 2017 , 45 (6) : 775-780 . |
| MLA | 熊贤祝 等. "函数型数据下条件分位数的经验似然推断" . | 福州大学学报（自然科学版） 45 . 6 (2017) : 775-780 . |
| APA | 熊贤祝 , 周培钦 . 函数型数据下条件分位数的经验似然推断 . | 福州大学学报（自然科学版） , 2017 , 45 (6) , 775-780 . |
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