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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 :
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 :
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 et al. "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 :
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 et al. "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 :
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 :
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 et al. "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 :
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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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 :
Modelling the covariance structure of multivariate longitudinal data is more challenging than its univariate counterpart, owing to the complex correlated structure among multiple responses. Furthermore, there are little methods focusing on the robustness of estimating the corresponding correlation matrix. In this paper, we propose an alternative Cholesky block decomposition (ACBD) for the covariance matrix of multivariate longitudinal data. The new unconstrained parameterization is capable to automatically eliminate the positive definiteness constraint of the covariance matrix and robustly estimate the correlation matrix with respect to the model misspecifications of the nested prediction error covariance matrices. The entries of the new decomposition are modelled by regression models, and the maximum likelihood estimators of the regression parameters in joint mean-covariance models are computed by a quasi-Fisher iterative algorithm. The resulting estimators are shown to be consistent and asymptotically normal. Simulations and real data analysis illustrate that the new method performs well.
Keyword :
maximum likelihood estimation maximum likelihood estimation multivariate longitudinal data multivariate longitudinal data Correlation matrix Correlation matrix Cholesky decomposition Cholesky decomposition robust estimation robust estimation
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GB/T 7714 | Lu, Fei , Xue, Liugen , Hu, Yuping . Robust estimation for the correlation matrix of multivariate longitudinal data [J]. | JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION , 2020 , 90 (13) : 2473-2496 . |
MLA | Lu, Fei et al. "Robust estimation for the correlation matrix of multivariate longitudinal data" . | JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 90 . 13 (2020) : 2473-2496 . |
APA | Lu, Fei , Xue, Liugen , Hu, Yuping . Robust estimation for the correlation matrix of multivariate longitudinal data . | JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION , 2020 , 90 (13) , 2473-2496 . |
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Abstract :
Semiparametric generalized varying coefficient partially linear models with longitudinal data arise in contemporary biology, medicine, and life science. In this paper, we consider a variable selection procedure based on the combination of the basis function approximations and quadratic inference functions with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency, sparsity, and asymptotic normality of the resulting estimators. The finite sample performance of the proposed methods is evaluated through extensive simulation studies and a real data analysis.
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GB/T 7714 | Zhang, Jinghua , Xue, Liugen . Penalized Quadratic Inference Function-Based Variable Selection for Generalized Partially Linear Varying Coefficient Models with Longitudinal Data [J]. | COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE , 2020 , 2020 . |
MLA | Zhang, Jinghua et al. "Penalized Quadratic Inference Function-Based Variable Selection for Generalized Partially Linear Varying Coefficient Models with Longitudinal Data" . | COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2020 (2020) . |
APA | Zhang, Jinghua , Xue, Liugen . Penalized Quadratic Inference Function-Based Variable Selection for Generalized Partially Linear Varying Coefficient Models with Longitudinal Data . | COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE , 2020 , 2020 . |
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