We develop an interquantile shrinkage estimation method to examine the underlying commonality structure of regression coefficients across various quantile levels for longitudinal data in a data-driven manner.This meth...We develop an interquantile shrinkage estimation method to examine the underlying commonality structure of regression coefficients across various quantile levels for longitudinal data in a data-driven manner.This method provides a deeper insight into the relationship between the response and covariates,leading to enhanced estimation efficiency and model interpretability.We propose a fused penalized generalized estimation equation(GEE)estimator with a non-crossing constraint,which automatically promotes constancy in estimates across neighboring quantiles.By accounting for within-subject correlation in longitudinal data,the GEE estimator improves estimation efficiency.We employ a nested alternating direction method of multiplier(ADMM)algorithm to minimize the regularized objective function.The asymptotic properties of the penalized estimators are established.Furthermore,in the presence of irrelevant predictors,we develop a doubly penalized GEE estimator to simultaneously select active variables and identify commonality across quantiles.Numerical studies demonstrate the superior performance of our proposed methods in terms of estimation efficiency.We illustrate the application of our methodologies by analyzing a longitudinal wage dataset.展开更多
1.Review The authors comprehensively review the current literature of sparse sufficient dimension reduction in three main settings:sparse estimation in sufficient dimension reduction when p<n;sparse estimation in s...1.Review The authors comprehensively review the current literature of sparse sufficient dimension reduction in three main settings:sparse estimation in sufficient dimension reduction when p<n;sparse estimation in sufficient dimension reduction when p>>n;variable screening in ultra-high dimensional setting.展开更多
In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properti...In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.展开更多
The estimates of the high-dimensional volatility matrix based on high-frequency data play a pivotal role in many financial applications.However,most existing studies have been built on the sub-Gaussian and cross-secti...The estimates of the high-dimensional volatility matrix based on high-frequency data play a pivotal role in many financial applications.However,most existing studies have been built on the sub-Gaussian and cross-sectional independence assumptions of microstructure noise,which are typically violated in the financial markets.In this paper,the authors proposed a new robust volatility matrix estimator,with very mild assumptions on the cross-sectional dependence and tail behaviors of the noises,and demonstrated that it can achieve the optimal convergence rate n-1/4.Furthermore,the proposed model offered better explanatory and predictive powers by decomposing the estimator into low-rank and sparse components,using an appropriate regularization procedure.Simulation studies demonstrated that the proposed estimator outperforms its competitors under various dependence structures of microstructure noise.Additionally,an extensive analysis of the high-frequency data for stocks in the Shenzhen Stock Exchange of China demonstrated the practical effectiveness of the estimator.展开更多
基金supported by National Key R&D Program of China(Grant No.2022YFA1003800)National Natural Science Foundation of China(Grant Nos.12301344,12471265,12231011 and 71988101)the Research Grant Council,University Grant Committee of Hong Kong Special Administrative Region(Grant No.14303622)。
文摘We develop an interquantile shrinkage estimation method to examine the underlying commonality structure of regression coefficients across various quantile levels for longitudinal data in a data-driven manner.This method provides a deeper insight into the relationship between the response and covariates,leading to enhanced estimation efficiency and model interpretability.We propose a fused penalized generalized estimation equation(GEE)estimator with a non-crossing constraint,which automatically promotes constancy in estimates across neighboring quantiles.By accounting for within-subject correlation in longitudinal data,the GEE estimator improves estimation efficiency.We employ a nested alternating direction method of multiplier(ADMM)algorithm to minimize the regularized objective function.The asymptotic properties of the penalized estimators are established.Furthermore,in the presence of irrelevant predictors,we develop a doubly penalized GEE estimator to simultaneously select active variables and identify commonality across quantiles.Numerical studies demonstrate the superior performance of our proposed methods in terms of estimation efficiency.We illustrate the application of our methodologies by analyzing a longitudinal wage dataset.
文摘1.Review The authors comprehensively review the current literature of sparse sufficient dimension reduction in three main settings:sparse estimation in sufficient dimension reduction when p<n;sparse estimation in sufficient dimension reduction when p>>n;variable screening in ultra-high dimensional setting.
基金supported by the National Natural Science Foundation of China(No.12571284,No.12171203)supported by the National Natural Science Foundation of China(No.12561051)+3 种基金the Fundamental Research Funds for the Central Universities(No.23JNQMX21)supported by the University-level scientific research project of Guangdong University of Foreign Studies(NO.299-GK25G301/25TS10)supported by a grant from National Natural Foundation of China(No.12171225)Yunnan Province Xing Dian Talent Support Program(YNWR-YLXZ-2018-020)。
文摘In this paper,we develop a robust variable selection procedure based on the exponential squared loss(ESL)function for the varying coefficient partially nonlinear model.Under certain conditions,some asymptotic properties of the proposed penalized ESL estimator are established.Meanwhile,the proposed procedure can automatically eliminate the irrelevant covariates,and simultaneously estimate the nonzero regression co-efficients.Furthermore,we apply the local quadratic approximation(LQA)and minorization–maximization(MM)algorithm to calculate the estimates of non-parametric and parametric parts,and introduce a data-driven method to select the tuning parameters.Simulation studies illustrate that the proposed method is more robust than the classical least squares technique when there are outliers in the dataset.Finally,we apply the proposed procedure to analyze the Boston housing price data.The results reveal that the proposed method has a better prediction ability.
基金supported by the National Natural Science Foundation of China under Grant Nos.72271232,71873137the MOE Project of Key Research Institute of Humanities and Social Sciences under Grant No.22JJD110001+1 种基金the support of Public Computing CloudRenmin University of China。
文摘The estimates of the high-dimensional volatility matrix based on high-frequency data play a pivotal role in many financial applications.However,most existing studies have been built on the sub-Gaussian and cross-sectional independence assumptions of microstructure noise,which are typically violated in the financial markets.In this paper,the authors proposed a new robust volatility matrix estimator,with very mild assumptions on the cross-sectional dependence and tail behaviors of the noises,and demonstrated that it can achieve the optimal convergence rate n-1/4.Furthermore,the proposed model offered better explanatory and predictive powers by decomposing the estimator into low-rank and sparse components,using an appropriate regularization procedure.Simulation studies demonstrated that the proposed estimator outperforms its competitors under various dependence structures of microstructure noise.Additionally,an extensive analysis of the high-frequency data for stocks in the Shenzhen Stock Exchange of China demonstrated the practical effectiveness of the estimator.
