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学者姓名：熊贤祝
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Abstract ：
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 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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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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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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Topological indices based on the distances between vertices(atoms) of a molecular graph are widely used for characterizing molecular graphs and their fragments, establishing relationships between structures and properties of molecules, predicting biological activity of chemical compounds, and making other chemical applications. Polyphenyls are a kind of macrocyclic aromatic hydrocarbons and their derivatives are very important organic chemicals, which can be used in organic synthesis, drug synthesis, heat exchanger, etc. In this paper we investigate the relationships between the Wiener index and other distance-based topological indices in the tree-like polyphenyl systems and obtain some exactly formulae on the relationships. (C) 2016 Elsevier Inc. All rights reserved.
Keyword ：
Degree distance Degree distance Polyphenyl chain Polyphenyl chain Szeged index Szeged index Topological index Topological index Wiener index Wiener index
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| GB/T 7714 | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Distance-based topological indices of the tree-like polyphenyl systems [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 281 : 233-242 . |
| MLA | Chen, Ailian 等. "Distance-based topological indices of the tree-like polyphenyl systems" . | APPLIED MATHEMATICS AND COMPUTATION 281 (2016) : 233-242 . |
| APA | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Distance-based topological indices of the tree-like polyphenyl systems . | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 281 , 233-242 . |
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The Wiener index W(G) and the edge-Wiener index W-e(G) of a graph G are defined as the sum of all distances between pairs of vertices in a graph G and the sum of all distances between pairs of edges in G, respectively. The Wiener index, due to its correlation with a large number of physico-chemical properties of organic molecules and its interesting and non-trivial mathematical properties, has been extensively studied in both theoretical and chemical literature. The edge-Wiener index of G is nothing but the Wiener index of the line graph of G. The concept of line graph has been found various applications in chemical research. In this paper, we show that if G is a catacondensed hexagonal system with h hexagons and has t linear segments S-1, S-2, ,S-t of lengths l(S-i) = l(i)(1 <= i <= t), then W-e(G) = 25/16W(G) + 1/16(120h(2) + 94h + 29) - 1/4 Sigma(t)(i=1)(l(i) - 1)(2). Our main result reduces the problems on the edge-Wiener index to those on the Wiener index in the catacondensed hexagonal systems, which makes the former ones easier. (C) 2015 Elsevier Inc. All rights reserved.
Keyword ：
Catacondensed hexagonal system Catacondensed hexagonal system Edge-Wiener index Edge-Wiener index Line graph Line graph Wiener index Wiener index
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| GB/T 7714 | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 273 : 1100-1106 . |
| MLA | Chen, Ailian 等. "Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems" . | APPLIED MATHEMATICS AND COMPUTATION 273 (2016) : 1100-1106 . |
| APA | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems . | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 273 , 1100-1106 . |
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