Research on species interactions has generally assumed that species have a fixed interaction and therefore linear or non-linear parametric regression models (e.g. exponential, logistic) have been widely used to descri...Research on species interactions has generally assumed that species have a fixed interaction and therefore linear or non-linear parametric regression models (e.g. exponential, logistic) have been widely used to describe the species interaction. However, these models that describe the relationship between interacting species as a specific functional response might not be appropriate for real biological communities, for instance, in a chaotic system, when the species relationship varies among different situations. To allow a more accurate description of the relationship, we developed a species correlation model with varying coefficient analysis, in which a non-parametric estimation is applied to identify, as a function of related factors, variation in the correlation coefficient. This was applied to a fig-fig wasp model system. When the effect of the factors on the relationship can be described with parameters, the new method reduces to traditional parametric correlation analysis. In this way, the new method is more general and flexible for empirical data analyses, but different by allowing investigation of whether a species interaction varies with respect to factors, and of the factors that maintain or change the species interaction. This method will have important applications in both theoretical and applied research (e.g. epidemiology, community management).展开更多
For analyzing correlated binary data with high-dimensional covariates,we,in this paper,propose a two-stage shrinkage approach.First,we construct a weighted least-squares(WLS) type function using a special weighting sc...For analyzing correlated binary data with high-dimensional covariates,we,in this paper,propose a two-stage shrinkage approach.First,we construct a weighted least-squares(WLS) type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations(GEE) model.Second,we define a penalized WLS in the spirit of the adaptive LASSO for simultaneous variable selection and parameter estimation.The proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of clusters.Moreover,we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is misspecified.For the selection of tuning parameter,we develop a consistent penalized quadratic form(PQF) function criterion.The performance of the proposed method is assessed through a comparison with the existing methods and through an application to a crossover trial in a pain relief study.展开更多
Large dimensional predictors are often introduced in regressions to attenuate the possible modeling bias. We consider the stable direction recovery in single-index models in which we solely assume the response Y is in...Large dimensional predictors are often introduced in regressions to attenuate the possible modeling bias. We consider the stable direction recovery in single-index models in which we solely assume the response Y is independent of the diverging dimensional predictors X when βτ 0 X is given, where β 0 is a p n × 1 vector, and p n →∞ as the sample size n →∞. We first explore sufficient conditions under which the least squares estimation β n0 recovers the direction β 0 consistently even when p n = o(√ n). To enhance the model interpretability by excluding irrelevant predictors in regressions, we suggest an e1-regularization algorithm with a quadratic constraint on magnitude of least squares residuals to search for a sparse estimation of β 0 . Not only can the solution β n of e1-regularization recover β 0 consistently, it also produces sufficiently sparse estimators which enable us to select "important" predictors to facilitate the model interpretation while maintaining the prediction accuracy. Further analysis by simulations and an application to the car price data suggest that our proposed estimation procedures have good finite-sample performance and are computationally efficient.展开更多
Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and t...Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and to select the most appropriate one. In this paper, we shall propose to use the empirical likelihood approach to evaluate these models. Simulation results and real life examples show that the empirical likelihood method is more powerful and more robust than some of the asymptotic method available in literature.展开更多
As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed...As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin's paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.展开更多
Existing groupwise dimension reduction requires given group structure to be non-overlapped. This confines its application scope. We aim at groupwise dimension reduction with overlapped group structure or even unknown ...Existing groupwise dimension reduction requires given group structure to be non-overlapped. This confines its application scope. We aim at groupwise dimension reduction with overlapped group structure or even unknown group structure. To this end, existing groupwise dimension reduction concept is extended to be compatible with overlapped group structure. Then, the envelope method is ameliorated to deal with overlapped groupwise dimension reduction. As an application, Gaussian graphic model is employed to estimate the structure between predictors when the group structure is not given, and the amended envelope method is used for groupwise dimension reduction with graphic structure. Furthermore, the rationale of the proposed estimation procedure is explained at the population level and the estimation consistency is proved at the sample level. Finally, the finite sample performance of the proposed methods is examined via numerical simulations and a body fat data analysis.展开更多
基金supported by the National Basic Research Program of China (2007CB411600)Na-tional Natural Science Foundation of China (30670272, 30770500 and 10761010)+5 种基金the Natural Science Foundation of Yunnan Province (2009- CD104)the West Light Foundation of the Chinese Academy of SciencesSpecial Fund for the Excellent Youth of the Chinese Academy of Sciences (KSCX2-EW-Q-9)State Key Laboratory of Genetic Resources and Evolu-tionthe National Social Science Foundation of China (08XTJ001)Research Grants Council of Hong Kong (HKBU2030/07P)
文摘Research on species interactions has generally assumed that species have a fixed interaction and therefore linear or non-linear parametric regression models (e.g. exponential, logistic) have been widely used to describe the species interaction. However, these models that describe the relationship between interacting species as a specific functional response might not be appropriate for real biological communities, for instance, in a chaotic system, when the species relationship varies among different situations. To allow a more accurate description of the relationship, we developed a species correlation model with varying coefficient analysis, in which a non-parametric estimation is applied to identify, as a function of related factors, variation in the correlation coefficient. This was applied to a fig-fig wasp model system. When the effect of the factors on the relationship can be described with parameters, the new method reduces to traditional parametric correlation analysis. In this way, the new method is more general and flexible for empirical data analyses, but different by allowing investigation of whether a species interaction varies with respect to factors, and of the factors that maintain or change the species interaction. This method will have important applications in both theoretical and applied research (e.g. epidemiology, community management).
基金supported by National Natural Science Foundation of China(Grant No.11201306)the Innovation Program of Shanghai Municipal Education Commission(Grant No.13YZ065)+2 种基金the Fundamental Research Project of Shanghai Normal University(Grant No.SK201207)the scholarship under the State Scholarship Fund by the China Scholarship Council in 2011the Research Grant Council of Hong Kong, Hong Kong,China(Grant No.#HKBU2028/10P)
文摘For analyzing correlated binary data with high-dimensional covariates,we,in this paper,propose a two-stage shrinkage approach.First,we construct a weighted least-squares(WLS) type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations(GEE) model.Second,we define a penalized WLS in the spirit of the adaptive LASSO for simultaneous variable selection and parameter estimation.The proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of clusters.Moreover,we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is misspecified.For the selection of tuning parameter,we develop a consistent penalized quadratic form(PQF) function criterion.The performance of the proposed method is assessed through a comparison with the existing methods and through an application to a crossover trial in a pain relief study.
基金supported by National Natural Science Foundation of China (Grant No. 10701035)Chen Guang Project of Shanghai Education Development Foundation (Grant No. 2007CG33)+1 种基金supported by Research Grants Council of Hong KongFaculty Research Grant from Hong Kong Baptist University
文摘Large dimensional predictors are often introduced in regressions to attenuate the possible modeling bias. We consider the stable direction recovery in single-index models in which we solely assume the response Y is independent of the diverging dimensional predictors X when βτ 0 X is given, where β 0 is a p n × 1 vector, and p n →∞ as the sample size n →∞. We first explore sufficient conditions under which the least squares estimation β n0 recovers the direction β 0 consistently even when p n = o(√ n). To enhance the model interpretability by excluding irrelevant predictors in regressions, we suggest an e1-regularization algorithm with a quadratic constraint on magnitude of least squares residuals to search for a sparse estimation of β 0 . Not only can the solution β n of e1-regularization recover β 0 consistently, it also produces sufficiently sparse estimators which enable us to select "important" predictors to facilitate the model interpretation while maintaining the prediction accuracy. Further analysis by simulations and an application to the car price data suggest that our proposed estimation procedures have good finite-sample performance and are computationally efficient.
基金supported by Guangdong Natural Science Foundation (Grant No.2008276)a grant from the Research Grants Council of Hong Kong,China
文摘Value at Risk (VaR) is a basic and very useful tool in measuring market risks. Numerous VaR models have been proposed in literature. Therefore, it is of great interest to evaluate the efficiency of these models, and to select the most appropriate one. In this paper, we shall propose to use the empirical likelihood approach to evaluate these models. Simulation results and real life examples show that the empirical likelihood method is more powerful and more robust than some of the asymptotic method available in literature.
基金supported by the National Natural Science Foundation of China under Grant Nos.11501354,11201499,11301309 and 714732802015 Shanghai Young Faculty Training Program under Grant No.A1A-6119-15-003
文摘As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin's paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.
基金supported by a grant from the University Grant Council of Hong Kong of ChinaNational Natural Science Foundation of China (Grant No. 11371013)Tian Yuan Foundation for Mathematics
文摘Existing groupwise dimension reduction requires given group structure to be non-overlapped. This confines its application scope. We aim at groupwise dimension reduction with overlapped group structure or even unknown group structure. To this end, existing groupwise dimension reduction concept is extended to be compatible with overlapped group structure. Then, the envelope method is ameliorated to deal with overlapped groupwise dimension reduction. As an application, Gaussian graphic model is employed to estimate the structure between predictors when the group structure is not given, and the amended envelope method is used for groupwise dimension reduction with graphic structure. Furthermore, the rationale of the proposed estimation procedure is explained at the population level and the estimation consistency is proved at the sample level. Finally, the finite sample performance of the proposed methods is examined via numerical simulations and a body fat data analysis.
