A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variabl...A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.展开更多
In clinical research,subgroup analysis can help identify patient groups that respond better or worse to specific treatments,improve therapeutic effect and safety,and is of great significance in precision medicine.This...In clinical research,subgroup analysis can help identify patient groups that respond better or worse to specific treatments,improve therapeutic effect and safety,and is of great significance in precision medicine.This article considers subgroup analysis methods for longitudinal data containing multiple covariates and biomarkers.We divide subgroups based on whether a linear combination of these biomarkers exceeds a predetermined threshold,and assess the heterogeneity of treatment effects across subgroups using the interaction between subgroups and exposure variables.Quantile regression is used to better characterize the global distribution of the response variable and sparsity penalties are imposed to achieve variable selection of covariates and biomarkers.The effectiveness of our proposed methodology for both variable selection and parameter estimation is verified through random simulations.Finally,we demonstrate the application of this method by analyzing data from the PA.3 trial,further illustrating the practicality of the method proposed in this paper.展开更多
In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that th...In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.展开更多
In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we prop...In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test.展开更多
We propose a robust estimation procedure based on local Walsh-average regression(LWR) for single-index models. Our novel method provides a root-n consistent estimate of the single-index parameter under some mild regul...We propose a robust estimation procedure based on local Walsh-average regression(LWR) for single-index models. Our novel method provides a root-n consistent estimate of the single-index parameter under some mild regularity conditions;the estimate of the unknown link function converges at the usual rate for the nonparametric estimation of a univariate covariate. We theoretically demonstrate that the new estimators show significant efficiency gain across a wide spectrum of non-normal error distributions and have almost no loss of efficiency for the normal error. Even in the worst case, the asymptotic relative efficiency(ARE) has a lower bound compared with the least squares(LS) estimates;the lower bounds of the AREs are 0.864 and 0.8896 for the single-index parameter and nonparametric function, respectively. Moreover, the ARE of the proposed LWR-based approach versus the ARE of the LS-based method has an expression that is closely related to the ARE of the signed-rank Wilcoxon test as compared with the t-test. In addition, to obtain a sparse estimate of the single-index parameter, we develop a variable selection procedure by combining the estimation method with smoothly clipped absolute deviation penalty;this procedure is shown to possess the oracle property. We also propose a Bayes information criterion(BIC)-type criterion for selecting the tuning parameter and further prove its ability to consistently identify the true model. We conduct some Monte Carlo simulations and a real data analysis to illustrate the finite sample performance of the proposed methods.展开更多
Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump poi...Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.展开更多
Different models have been proposed in corporate finance literature for predicting the risk of firm＇s bankruptcy and insolvency. In spite of the large amount of empirical findings, significant issues are still unsolv...Different models have been proposed in corporate finance literature for predicting the risk of firm＇s bankruptcy and insolvency. In spite of the large amount of empirical findings, significant issues are still unsolved. In this paper, the authors developed dynamic statistical models for bankruptcy prediction of Italian firms in the industrial sector by using financial indicators. The model specification has been obtained via different variable selection techniques, and the predictive accuracy of the proposed default risk models has been evaluated at various horizons by means of different accuracy measures. The reached results give evidence that dynamic models have a better performance in any of the considered scenarios.展开更多
Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. ...Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. In recent years, researchers’ research on government credibility has mostly focused on exploring theories and mechanisms, with little empirical research on this topic. This article intends to apply variable selection models in the field of social statistics to the issue of government credibility, in order to achieve empirical research on government credibility and explore its core influencing factors from a statistical perspective. Specifically, this article intends to use four regression-analysis-based methods and three random-forest-based methods to study the influencing factors of government credibility in various provinces in China, and compare the performance of these seven variable selection methods in different dimensions. The research results show that there are certain differences in simplicity, accuracy, and variable importance ranking among different variable selection methods, which present different importance in the study of government credibility issues. This study provides a methodological reference for variable selection models in the field of social science research, and also offers a multidimensional comparative perspective for analyzing the influencing factors of government credibility.展开更多
This paper employs the SCAD-penalized least squares method to simultaneously select variables and estimate the coefficients for high-dimensional covariate adjusted linear regression models.The distorted variables are ...This paper employs the SCAD-penalized least squares method to simultaneously select variables and estimate the coefficients for high-dimensional covariate adjusted linear regression models.The distorted variables are assumed to be contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate.The authors show that under some appropriate conditions,the SCAD-penalized least squares estimator has the so called "oracle property".In addition,the authors also suggest a BIC criterion to select the tuning parameter,and show that BIC criterion is able to identify the true model consistently for the covariate adjusted linear regression models.Simulation studies and a real data are used to illustrate the efficiency of the proposed estimation algorithm.展开更多
主要研究四参数Logistic项目反应理论框架下潜在回归模型系数的贝叶斯变量选择方法。潜在回归模型是项目反应模型的扩展,该模型以学生潜在能力为响应变量,以观测变量(人口学特征、心理特质等)为解释变量建立回归模型。首先,通过将四参数...主要研究四参数Logistic项目反应理论框架下潜在回归模型系数的贝叶斯变量选择方法。潜在回归模型是项目反应模型的扩展,该模型以学生潜在能力为响应变量,以观测变量(人口学特征、心理特质等)为解释变量建立回归模型。首先,通过将四参数Logistic模型嵌入线性回归模型内,建立潜在回归模型;其次,通过对潜在回归系数引入Laplace、Horseshoe和Horseshoe+三类收缩先验,进行参数估计和变量选择;最后,通过模拟实验,与传统Metropolis-Hasting算法进行比较,以评估Hamiltonian Monte Carlo抽样方法的性能,实验结果表明,所采用的Hamiltonian Monte Carlo估计方法比Metropolis-Hasting算法更高效、更灵活。采用PISA-2018数据集开展实证研究,验证了所提出潜在回归模型及估计方法的有效性与实用性。展开更多
基金Zhou's research was partially supported by the foundations of NatioiMd Natural Science (10471140) and (10571169) of China.
文摘A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.
基金Supported by the Natural Science Foundation of Fujian Province(2022J011177,2024J01903)the Key Project of Fujian Provincial Education Department(JZ230054)。
文摘In clinical research,subgroup analysis can help identify patient groups that respond better or worse to specific treatments,improve therapeutic effect and safety,and is of great significance in precision medicine.This article considers subgroup analysis methods for longitudinal data containing multiple covariates and biomarkers.We divide subgroups based on whether a linear combination of these biomarkers exceeds a predetermined threshold,and assess the heterogeneity of treatment effects across subgroups using the interaction between subgroups and exposure variables.Quantile regression is used to better characterize the global distribution of the response variable and sparsity penalties are imposed to achieve variable selection of covariates and biomarkers.The effectiveness of our proposed methodology for both variable selection and parameter estimation is verified through random simulations.Finally,we demonstrate the application of this method by analyzing data from the PA.3 trial,further illustrating the practicality of the method proposed in this paper.
基金supported by National Natural Science Foundation of China (Grant No.10971007)Beijing Natural Science Fund (Grant No. 1072003)Science Fund of Beijing Education Committee
文摘In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.10271033)the Education Bureau of Guangzhou Muni cipal Government(Grant No.2004)the Science and Technology Bureau of Guangzhou Municipal Government(Grant No.2004J1-C0333).
文摘In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test.
基金partially supported by National Natural Science Foundation of China(Grant Nos.11801168,11801169,11571055 and 11671059)the Natural Science Foundation of Hunan Province(Grant No.2018JJ3322)
文摘We propose a robust estimation procedure based on local Walsh-average regression(LWR) for single-index models. Our novel method provides a root-n consistent estimate of the single-index parameter under some mild regularity conditions;the estimate of the unknown link function converges at the usual rate for the nonparametric estimation of a univariate covariate. We theoretically demonstrate that the new estimators show significant efficiency gain across a wide spectrum of non-normal error distributions and have almost no loss of efficiency for the normal error. Even in the worst case, the asymptotic relative efficiency(ARE) has a lower bound compared with the least squares(LS) estimates;the lower bounds of the AREs are 0.864 and 0.8896 for the single-index parameter and nonparametric function, respectively. Moreover, the ARE of the proposed LWR-based approach versus the ARE of the LS-based method has an expression that is closely related to the ARE of the signed-rank Wilcoxon test as compared with the t-test. In addition, to obtain a sparse estimate of the single-index parameter, we develop a variable selection procedure by combining the estimation method with smoothly clipped absolute deviation penalty;this procedure is shown to possess the oracle property. We also propose a Bayes information criterion(BIC)-type criterion for selecting the tuning parameter and further prove its ability to consistently identify the true model. We conduct some Monte Carlo simulations and a real data analysis to illustrate the finite sample performance of the proposed methods.
文摘Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.
文摘Different models have been proposed in corporate finance literature for predicting the risk of firm＇s bankruptcy and insolvency. In spite of the large amount of empirical findings, significant issues are still unsolved. In this paper, the authors developed dynamic statistical models for bankruptcy prediction of Italian firms in the industrial sector by using financial indicators. The model specification has been obtained via different variable selection techniques, and the predictive accuracy of the proposed default risk models has been evaluated at various horizons by means of different accuracy measures. The reached results give evidence that dynamic models have a better performance in any of the considered scenarios.
文摘Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. In recent years, researchers’ research on government credibility has mostly focused on exploring theories and mechanisms, with little empirical research on this topic. This article intends to apply variable selection models in the field of social statistics to the issue of government credibility, in order to achieve empirical research on government credibility and explore its core influencing factors from a statistical perspective. Specifically, this article intends to use four regression-analysis-based methods and three random-forest-based methods to study the influencing factors of government credibility in various provinces in China, and compare the performance of these seven variable selection methods in different dimensions. The research results show that there are certain differences in simplicity, accuracy, and variable importance ranking among different variable selection methods, which present different importance in the study of government credibility issues. This study provides a methodological reference for variable selection models in the field of social science research, and also offers a multidimensional comparative perspective for analyzing the influencing factors of government credibility.
基金supported by the National Natural Science Foundation of China under Grant Nos.11471029,11101014,61273221 and 11171010the Beijing Natural Science Foundation under Grant Nos.1142002 and 1112001+1 种基金the Science and Technology Project of Beijing Municipal Education Commission under Grant No.KM201410005010the Research Fund for the Doctoral Program of Beijing University of Technology under Grant No.006000543114550
文摘This paper employs the SCAD-penalized least squares method to simultaneously select variables and estimate the coefficients for high-dimensional covariate adjusted linear regression models.The distorted variables are assumed to be contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate.The authors show that under some appropriate conditions,the SCAD-penalized least squares estimator has the so called "oracle property".In addition,the authors also suggest a BIC criterion to select the tuning parameter,and show that BIC criterion is able to identify the true model consistently for the covariate adjusted linear regression models.Simulation studies and a real data are used to illustrate the efficiency of the proposed estimation algorithm.
文摘主要研究四参数Logistic项目反应理论框架下潜在回归模型系数的贝叶斯变量选择方法。潜在回归模型是项目反应模型的扩展,该模型以学生潜在能力为响应变量,以观测变量(人口学特征、心理特质等)为解释变量建立回归模型。首先,通过将四参数Logistic模型嵌入线性回归模型内,建立潜在回归模型;其次,通过对潜在回归系数引入Laplace、Horseshoe和Horseshoe+三类收缩先验,进行参数估计和变量选择;最后,通过模拟实验,与传统Metropolis-Hasting算法进行比较,以评估Hamiltonian Monte Carlo抽样方法的性能,实验结果表明,所采用的Hamiltonian Monte Carlo估计方法比Metropolis-Hasting算法更高效、更灵活。采用PISA-2018数据集开展实证研究,验证了所提出潜在回归模型及估计方法的有效性与实用性。
基金supported by National Natural Science Foundation of China (10471136 and 10671189)the Knowledge Innovation Program of the Chinese Academy of Sciences (KJCX3-SYW-S02)
