This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression model...This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.展开更多
The excellent vectoring characteristic of Dual Synthetic Jet(DSJ)provides a new control strategy for the active flow control,such as thrust vectoring control,large area cooling,separated flow control and so on.For inc...The excellent vectoring characteristic of Dual Synthetic Jet(DSJ)provides a new control strategy for the active flow control,such as thrust vectoring control,large area cooling,separated flow control and so on.For incompressible flow,the influence relation of source variables,such as structure parameters of actuators,driving parameters and material attributes of piezoelectric vibrating diaphragm,on the vectoring DSJ and a theoretical model are established based on theoretical and regression analysis,which are all verified by numerical simulations.The two synthetic jets can be deemed as a main flow with a higher jet velocity and a disturbing flow with a lower jet velocity.The results indicate that the influence factors contain the low-pressure area formed at the exit of the disturbing flow,which could promote the vectoring deflection,and the impact effect of the disturbing flow and the suppressive effect of the main flow with the effect of restraining the vectoring deflection.The vectoring angle is a complex parameter coupled by all source variables.The detailed theoretical model,whose error is controlled within 3.6 degrees,can be used to quantitatively assess the vectoring feature of DSJ and thus to provide a guidance for designing the control law applied in the active flow control.展开更多
Functional magnetic resonance imaging（fMRI）is an in-vivo non-invasive technique for measuring brain activity with excellent spatial and good temporal resolution.Without performing explicit tasks,resting-state fMRI（...Functional magnetic resonance imaging（fMRI）is an in-vivo non-invasive technique for measuring brain activity with excellent spatial and good temporal resolution.Without performing explicit tasks,resting-state fMRI（rfMRI）is widely used to map the functional connectivity network（FCN）,which refers to a large-scale network of interdependent or functionally connected brain regions and it could be detected by using different algorithms（Zuo and Xing, 2014）.ciation CAS （2016084）, Guangxi Bagui Scholarship, the Natural Science Foundation of China （81471740, 81220108014）, the Major Project of National Social Science Foundation of China （14ZDB161）, Beijing Municipal Science and Tech Commission （Z161100002616023, Z161100000216152） and the National R＆D Infrastructure and Facility Development Program ＂Fundamental Science Data Sharing Platform＂ （DKA2017-12-02-21）.展开更多
文摘This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.
基金supported by the National Natural Science Foundation of China(Nos.11972369 and 11872374)。
文摘The excellent vectoring characteristic of Dual Synthetic Jet(DSJ)provides a new control strategy for the active flow control,such as thrust vectoring control,large area cooling,separated flow control and so on.For incompressible flow,the influence relation of source variables,such as structure parameters of actuators,driving parameters and material attributes of piezoelectric vibrating diaphragm,on the vectoring DSJ and a theoretical model are established based on theoretical and regression analysis,which are all verified by numerical simulations.The two synthetic jets can be deemed as a main flow with a higher jet velocity and a disturbing flow with a lower jet velocity.The results indicate that the influence factors contain the low-pressure area formed at the exit of the disturbing flow,which could promote the vectoring deflection,and the impact effect of the disturbing flow and the suppressive effect of the main flow with the effect of restraining the vectoring deflection.The vectoring angle is a complex parameter coupled by all source variables.The detailed theoretical model,whose error is controlled within 3.6 degrees,can be used to quantitatively assess the vectoring feature of DSJ and thus to provide a guidance for designing the control law applied in the active flow control.
基金supported by the National Basic Research Program(2015CB351702)the Youth Innovation Promotion Association CAS(2016084)+3 种基金Guangxi Bagui Scholarship,the Natural Science Foundation of China(81471740,81220108014)the Major Project of National Social Science Foundation of China(14ZDB161)Beijing Municipal Science and Tech Commission(Z161100002616023,Z161100000216152)the National R&D Infrastructure and Facility Development Program“Fundamental Science Data Sharing Platform”(DKA2017-12-02-21)
文摘Functional magnetic resonance imaging（fMRI）is an in-vivo non-invasive technique for measuring brain activity with excellent spatial and good temporal resolution.Without performing explicit tasks,resting-state fMRI（rfMRI）is widely used to map the functional connectivity network（FCN）,which refers to a large-scale network of interdependent or functionally connected brain regions and it could be detected by using different algorithms（Zuo and Xing, 2014）.ciation CAS （2016084）, Guangxi Bagui Scholarship, the Natural Science Foundation of China （81471740, 81220108014）, the Major Project of National Social Science Foundation of China （14ZDB161）, Beijing Municipal Science and Tech Commission （Z161100002616023, Z161100000216152） and the National R＆D Infrastructure and Facility Development Program ＂Fundamental Science Data Sharing Platform＂ （DKA2017-12-02-21）.
