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摘要 ：
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.
关键词 ：
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
引用：
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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 . |
| MLA | Hu, Yuping et al. "Statistical inference of varying-coefficient partial functional spatial autoregressive model" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS (2021) . |
| 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 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
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.
关键词 ：
Panel data Panel data Nonparametric component checking Nonparametric component checking Varying coefficient model Varying coefficient model Empirical likelihood Empirical likelihood
引用：
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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 . |
| MLA | Li, Wanbin et al. "An empirical likelihood check with varying coefficient fixed effect model with panel data" . | JOURNAL OF THE KOREAN STATISTICAL SOCIETY (2021) . |
| 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 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
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.
关键词 ：
Functional data analysis Functional data analysis group SCAD group SCAD oracle property oracle property robust estimation robust estimation variable selection variable selection
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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 . |
| MLA | Cai, Xiong et al. "Robust estimation and variable selection for function-on-scalar regression" . | CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE (2021) . |
| 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 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
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.
关键词 ：
functional data functional data penalized regression penalized regression robust procedures robust procedures
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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) . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
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.
关键词 ：
Adaptive factorization rank selection Adaptive factorization rank selection Deep learning Deep learning Inverse space sparse representation based classification Inverse space sparse representation based classification Non-negative matrix factorization Non-negative matrix factorization Tumor recognition Tumor recognition
引用：
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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 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
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.
关键词 ：
渐近正态性 渐近正态性 局部纠偏 局部纠偏 部分非线性变系数模型 部分非线性变系数模型 测量误差 测量误差 缺失数据 缺失数据
引用：
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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:A辑 , 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:A辑 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:A辑 , 2020 , 40 (2) , 460-474 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this article, we consider a new robust estimation procedure for functional linear models with both slope function and functional predictor approximated by functional principal component basis functions. A modified Huber's function with tail function substituted by the exponential squared loss (ESL) is applied to the estimation procedure for achieving robustness against outliers. The tuning parameters of the new estimation method are data-driven, which enables us to reach better robustness and efficiency than other robust methods in the presence of outliers or heavy-tailed error distribution. We will show that the resulting estimator for the slope function achieves the optimal convergence rate as the least-squares estimator does in the classical functional linear regression. The convergence rate of the prediction in terms of conditional mean squared prediction error is also established. The proposed method is illustrated with simulation studies and a real data example.
关键词 ：
Huber Huber functional linear models functional linear models functional principal component analysis functional principal component analysis exponential squared loss exponential squared loss Robust estimation Robust estimation
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| GB/T 7714 | Cai, Xiong , Xue, Liugen , Wang, Zhaoliang . Robust estimation with modified Huber's function for functional linear models [J]. | STATISTICS , 2020 , 54 (6) : 1276-1286 . |
| MLA | Cai, Xiong et al. "Robust estimation with modified Huber's function for functional linear models" . | STATISTICS 54 . 6 (2020) : 1276-1286 . |
| APA | Cai, Xiong , Xue, Liugen , Wang, Zhaoliang . Robust estimation with modified Huber's function for functional linear models . | STATISTICS , 2020 , 54 (6) , 1276-1286 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this article, we consider the problem of estimation of the single-index varying-coefficient model when covariates are not fully observed. By using the bias-correction and inverse selection probability methods, a weighted estimating equations estimator for the index parameters with missing covariates is constructed, and its asymptotic properties has been established. The local linear estimator for the coefficient functions is proved to converge at an optimal rate. Numerical studies based on simulation and application suggest that the proposed estimation procedure is powerful and easy to implement.
关键词 ：
Asymptotic properties Asymptotic properties Estimating equations Estimating equations Inverse probability weighting Inverse probability weighting Missing covariates data Missing covariates data Single-index varying-coefficient model Single-index varying-coefficient model
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| GB/T 7714 | Zhao, Yang , Xue, Liugen , Zhang, Jinghua et al. Single-index varying-coefficient models with missing covariates at random [J]. | COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION , 2020 . |
| MLA | Zhao, Yang et al. "Single-index varying-coefficient models with missing covariates at random" . | COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION (2020) . |
| APA | Zhao, Yang , Xue, Liugen , Zhang, Jinghua , Liu, Juanfang . Single-index varying-coefficient models with missing covariates at random . | COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION , 2020 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
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.
关键词 ：
empirical likelihood inference empirical likelihood inference panel data panel data Varying coefficient fixed effect models Varying coefficient fixed effect models
引用：
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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 . |
| MLA | Li, Wanbin et al. "Empirical likelihood based inference for varying coefficient panel data models with fixed effect" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS (2020) . |
| 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 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
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.
关键词 ：
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
引用：
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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 . |
| 导入链接 | NoteExpress RIS BibTex |
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