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学者姓名：薛留根
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Abstract ：
We introduce a variable selection procedure for function-on-function linear models with multiple functional predictors, using the functional principal component analysis (FPCA)-based estimation method with the group smoothly clipped absolute deviation regularization. This approach enables us to select significant functional predictors and estimate the bivariate functional coefficients simultaneously. A data-driven procedure is provided for choosing the tuning parameters of the proposed method to achieve high efficiency. We construct FPCA-based estimators for the bivariate functional coefficients using the proposed regularization method. Under some mild conditions, we establish the estimation and selection consistencies of the proposed procedure. Simulation studies are carried out to illustrate the finite-sample performance of the proposed method. The results show that our method is highly effective in identifying the relevant functional predictors and in estimating the bivariate functional coefficients. Furthermore, the proposed method is demonstrated in a real-data example by investigating the association between ocean temperature and several water variables.
Keyword ：
group SCAD group SCAD functional principal component analysis functional principal component analysis selection consistency selection consistency regularization regularization Functional data analysis Functional data analysis
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| GB/T 7714 | Cai, Xiong , Xue, Liugen , Cao, Jiguo . VARIABLE SELECTION FOR MULTIPLE FUNCTION-ON-FUNCTION LINEAR REGRESSION [J]. | STATISTICA SINICA , 2022 , 32 (3) : 1435-1465 . |
| MLA | Cai, Xiong 等. "VARIABLE SELECTION FOR MULTIPLE FUNCTION-ON-FUNCTION LINEAR REGRESSION" . | STATISTICA SINICA 32 . 3 (2022) : 1435-1465 . |
| APA | Cai, Xiong , Xue, Liugen , Cao, Jiguo . VARIABLE SELECTION FOR MULTIPLE FUNCTION-ON-FUNCTION LINEAR REGRESSION . | STATISTICA SINICA , 2022 , 32 (3) , 1435-1465 . |
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Abstract ：
Semiparametric models are often used to analyze panel data for a good trade-off between parsimony and flexibility. In this paper, we investigate a fixed effect model with a possible varying coefficient component. On the basis of empirical likelihood method, the coefficient functions are estimated as well as their confidence intervals. The estimation procedures are easily implemented. An important problem of the statistical inference with the varying coefficient model is to check the constant coefficient about the regression functions. We further develop checking procedures by constructing empirical likelihood ratio statistics and establishing the Wilks theorems. Finally, some numerical simulations and a real data analysis is presented to assess the finite sample performance.
Keyword ：
Panel data Panel data Nonparametric component checking Nonparametric component checking Varying coefficient model Varying coefficient model Empirical likelihood Empirical likelihood
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| GB/T 7714 | Li, Wanbin , Xue, Liugen , Zhao, Peixin . An empirical likelihood check with varying coefficient fixed effect model with panel data [J]. | JOURNAL OF THE KOREAN STATISTICAL SOCIETY , 2021 , 51 (1) : 198-222 . |
| MLA | Li, Wanbin 等. "An empirical likelihood check with varying coefficient fixed effect model with panel data" . | JOURNAL OF THE KOREAN STATISTICAL SOCIETY 51 . 1 (2021) : 198-222 . |
| APA | Li, Wanbin , Xue, Liugen , Zhao, Peixin . An empirical likelihood check with varying coefficient fixed effect model with panel data . | JOURNAL OF THE KOREAN STATISTICAL SOCIETY , 2021 , 51 (1) , 198-222 . |
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Abstract ：
Function-on-scalar regression is commonly used to model the dynamic behaviour of a set of scalar predictors of interest on the functional response. In this article, we develop a robust variable selection procedure for function-on-scalar regression with a large number of scalar predictors based on exponential squared loss combined with the group smoothly clipped absolute deviation regularization method. The proposed procedure simultaneously selects relevant predictors and provides estimates for the functional coefficients, and achieves robustness and efficiency using tuning parameters selected by a data-driven procedure. Under reasonable conditions, we establish the asymptotic properties of the proposed estimators, including estimation consistency and the oracle property. The finite-sample performance of the proposed method is investigated with simulation studies. The proposed method is also demonstrated with a real diffusion tensor imaging data example.
Keyword ：
variable selection variable selection robust estimation robust estimation oracle property oracle property group SCAD group SCAD Functional data analysis Functional data analysis
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| GB/T 7714 | Cai, Xiong , Xue, Liugen , Ca, Jiguo . Robust estimation and variable selection for function-on-scalar regression [J]. | CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE , 2021 , 50 (1) : 162-179 . |
| MLA | Cai, Xiong 等. "Robust estimation and variable selection for function-on-scalar regression" . | CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 50 . 1 (2021) : 162-179 . |
| APA | Cai, Xiong , Xue, Liugen , Ca, Jiguo . Robust estimation and variable selection for function-on-scalar regression . | CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE , 2021 , 50 (1) , 162-179 . |
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Abstract ：
Function-on-function linear regression is an essential tool in characterizing the linear relationship between a functional response and a functional predictor. However, most of the estimation methods for this model are based on the least-squares procedure, which is sensitive to atypical observations. In this paper, we present a robust method for the function-on-function linear model using M-estimation and penalized spline regression. A fast iterative algorithm is provided to compute the estimates. The efficiency of the proposed robust penalized M-estimator is investigated with several simulation studies in comparison with the conventional method. We demonstrate the performance of the proposed robust method with two real data examples in a capital bike-sharing study and a Hawaii ocean time-series program.
Keyword ：
functional data functional data robust procedures robust procedures penalized regression penalized regression
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| GB/T 7714 | Cai, Xiong , Xue, Liugen , Cao, Jiguo . Robust penalized M-estimation for function-on-function linear regression [J]. | STAT , 2021 , 10 (1) . |
| MLA | Cai, Xiong 等. "Robust penalized M-estimation for function-on-function linear regression" . | STAT 10 . 1 (2021) . |
| APA | Cai, Xiong , Xue, Liugen , Cao, Jiguo . Robust penalized M-estimation for function-on-function linear regression . | STAT , 2021 , 10 (1) . |
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Abstract ：
The nonnegative matrix factorization (NMF) has been widely used because it can accomplish both feature representation learning and dimension reduction. However, there are two critical and challenging issues affecting the performance of NMF models. One is the selection of matrix factorization rank, while most of the existing methods are based on experiments or experience. For tackling this issue, an adaptive and stable NMF model is constructed based on an adaptive factorization rank selection (AFRS) strategy, which skillfully and simply integrates a row constraint similar to the generalized elastic net. The other is the sensitivity to the initial value of the iteration, which seriously affects the result of matrix factorization. This issue is alleviated by complementing NMF and deep learning each other and avoiding complex network structure. The proposed NMF model is called deep AFRS-NMF model for short, and the corresponding optimization solution, convergence and stability are analyzed. Moreover, the statistical consistency is discussed between the rank obtained by the proposed model and the ideal rank. The performance of the proposed deep AFRS-NMF model is demonstrated by applying in genetic data-based tumor recognition. Experiments show that the factorization rank obtained by the deep AFRS-NMF model is stable and superior to classical and state-of-the-art methods.
Keyword ：
Inverse space sparse representation based classification Inverse space sparse representation based classification Tumor recognition Tumor recognition Non-negative matrix factorization Non-negative matrix factorization Deep learning Deep learning Adaptive factorization rank selection Adaptive factorization rank selection
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| GB/T 7714 | Yang, Xiaohui , Wu, Wenming , Xin, Xin et al. Adaptive factorization rank selection-based NMF and its application in tumor recognition [J]. | INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS , 2021 , 12 (9) : 2673-2691 . |
| MLA | Yang, Xiaohui et al. "Adaptive factorization rank selection-based NMF and its application in tumor recognition" . | INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 12 . 9 (2021) : 2673-2691 . |
| APA | Yang, Xiaohui , Wu, Wenming , Xin, Xin , Su, Limin , Xue, Liugen . Adaptive factorization rank selection-based NMF and its application in tumor recognition . | INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS , 2021 , 12 (9) , 2673-2691 . |
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Abstract ：
In this paper, based on spatial autoregression and partial functional linear regression, we introduce a new varying-coefficient partial functional spatial autoregressive model. The functional principal component analysis and B-spline are adopted to approximate the slope function and varying-coefficient functions respectively. Then, the instrumental variable method gives final estimators. Under some regular conditions, we further study the asymptotic normality of the parameter and the convergence rates of slope function and coefficient functions. Lastly, the finite sample performance of the proposed methodology is evaluated by simulation studies and a practical data example.
Keyword ：
varying-coefficient partial functional regressive model varying-coefficient partial functional regressive model B-spline B-spline spatial autoregression spatial autoregression instrumental variable instrumental variable functional principal component analysis functional principal component analysis Functional data analysis Functional data analysis
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| GB/T 7714 | Hu, Yuping , Wang, Yilun , Zhang, Liying et al. Statistical inference of varying-coefficient partial functional spatial autoregressive model [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2021 , 52 (14) : 4960-4980 . |
| MLA | Hu, Yuping et al. "Statistical inference of varying-coefficient partial functional spatial autoregressive model" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 52 . 14 (2021) : 4960-4980 . |
| APA | Hu, Yuping , Wang, Yilun , Zhang, Liying , Xue, Liugen . Statistical inference of varying-coefficient partial functional spatial autoregressive model . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2021 , 52 (14) , 4960-4980 . |
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Abstract ：
在广义估计方程框架下,发展了一类灵活的回归模型来参数化协方差结构.通过合并广泛使用的修正的Cholesky分解和滑动平均Cholesky分解,得到自回归滑动平均Cholesky分解.该分解能够参数化更一般的协方差结构,且其输入具有清晰的统计解释.对这些输入建立回归模型,并利用拟Fisher迭代算法估计回归系数.均值和协方差模型中的参数估计皆具有相合性和渐近正态性.最后通过模拟研究考察了所提方法的有限样本表现.
Keyword ：
Cholesky分解 Cholesky分解 广义估计方程 广义估计方程 纵向数据 纵向数据
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| GB/T 7714 | 芦飞 , 薛留根 . 纵向数据下均值协方差联合建模中的ARMA Cholesky因子模型 [J]. | 数学的实践与认识 , 2020 , 50 (1) : 183-187 . |
| MLA | 芦飞 et al. "纵向数据下均值协方差联合建模中的ARMA Cholesky因子模型" . | 数学的实践与认识 50 . 1 (2020) : 183-187 . |
| APA | 芦飞 , 薛留根 . 纵向数据下均值协方差联合建模中的ARMA Cholesky因子模型 . | 数学的实践与认识 , 2020 , 50 (1) , 183-187 . |
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Abstract ：
该文研究了响应变量缺失下半参数部分非线性变系数EV模型的统计推断问题,利用逆概率加权局部纠偏profile最小二乘法构造了模型中非参数分量和参数分量的估计,证明了估计量的渐近正态性.通过数值模拟和实际数据分析,验证了所提出的估计方法是有效的.
Keyword ：
缺失数据 缺失数据 局部纠偏 局部纠偏 渐近正态性 渐近正态性 测量误差 测量误差 部分非线性变系数模型 部分非线性变系数模型
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| GB/T 7714 | 马奕佳 , 薛留根 , 芦飞 . 缺失数据下部分非线性变系数EV模型的统计推断 [J]. | 数学物理学报 , 2020 , 40 (2) : 460-474 . |
| MLA | 马奕佳 et al. "缺失数据下部分非线性变系数EV模型的统计推断" . | 数学物理学报 40 . 2 (2020) : 460-474 . |
| APA | 马奕佳 , 薛留根 , 芦飞 . 缺失数据下部分非线性变系数EV模型的统计推断 . | 数学物理学报 , 2020 , 40 (2) , 460-474 . |
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Abstract ：
Variables selection and parameter estimation are of great significance in all regression analysis. A variety of approaches have been proposed to tackle this problem. Among those, the penalty-based shrinkage approach has been most popular for the ability to carry out the variable selection and parameter estimation simultaneously. However, not much work is available on the variable selection for the generalized partially models (GPLMs) with longitudinal data. In this paper, we proposed a variable selection procedure for GPLMs with longitudinal data. The inference is based on the SCAD-penalized quadratic inference functions, which is obtained after the B-spline approximating to non-parametric function in the model. The proposed approach efficiently utilized the within-cluster correlation information, which can improve estimating efficiency. The proposed approach also has the virtue of low computational cost. With the tuning parameter chosen by BIC, the correct model is identified with probability tends to 1. The resulted estimator of the parametric component is asymptotic to a normal distribution, and that of the non-parametric function achieves the optimal convergence rate. The performance of the proposed methods is evaluated through extensive simulation studies. A real data analysis shows that the proposed approach succeeds in excluding the insignificant variable.
Keyword ：
Quadratic inference functions Quadratic inference functions Longitudinal data Longitudinal data Variable selection Variable selection Generalized partially linear models Generalized partially linear models
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| GB/T 7714 | Zhang, Jinghua , Xue, Liugen . Variable selection for generalized partially linear models with longitudinal data [J]. | EVOLUTIONARY INTELLIGENCE , 2020 , 15 (4) : 2473-2483 . |
| MLA | Zhang, Jinghua et al. "Variable selection for generalized partially linear models with longitudinal data" . | EVOLUTIONARY INTELLIGENCE 15 . 4 (2020) : 2473-2483 . |
| APA | Zhang, Jinghua , Xue, Liugen . Variable selection for generalized partially linear models with longitudinal data . | EVOLUTIONARY INTELLIGENCE , 2020 , 15 (4) , 2473-2483 . |
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Abstract ：
In this paper, the empirical likelihood-based inference is investigated with varying coefficient panel data models with fixed effect. A naive empirical likelihood ratio is firstly proposed after the fixed effect is corrected. The maximum empirical likelihood estimators for the coefficient functions are derived as well as their asymptotic properties. Wilk's phenomenon of this naive empirical likelihood ratio is proven under a undersmoothing assumption. To avoid the requisition of undersmoothing and perform an efficient inference, a residual-adjusted empirical likelihood ratio is further suggested and shown as having a standard chi-square limit distribution, by which the confidence regions of the coefficient functions are constructed. Another estimators for the coefficient functions, together with their asymptotic properties, are considered by maximizing the residual-adjusted empirical log-likelihood function under an optimal bandwidth. The performances of these proposed estimators and confidence regions are assessed through numerical simulations and a real data analysis.
Keyword ：
Varying coefficient fixed effect models Varying coefficient fixed effect models empirical likelihood inference empirical likelihood inference panel data panel data
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| GB/T 7714 | Li, Wanbin , Xue, Liugen , Zhao, Peixin . Empirical likelihood based inference for varying coefficient panel data models with fixed effect [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2020 , 51 (14) : 4973-4990 . |
| MLA | Li, Wanbin et al. "Empirical likelihood based inference for varying coefficient panel data models with fixed effect" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 51 . 14 (2020) : 4973-4990 . |
| APA | Li, Wanbin , Xue, Liugen , Zhao, Peixin . Empirical likelihood based inference for varying coefficient panel data models with fixed effect . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2020 , 51 (14) , 4973-4990 . |
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