The article deals with optimality of combining ridge and principal component estimator.It is proved that combining ridge and principal componet estimate has several types of minimumvariance properties in the class of ...The article deals with optimality of combining ridge and principal component estimator.It is proved that combining ridge and principal componet estimate has several types of minimumvariance properties in the class of reduced dimension estimates and it also has minimum of orthogo-nal unchanged norm of covariance in the same class.展开更多
Gauss-Markov model is frequently used in data analysis;the analysis and estimation of its parameters is always a hot issue.Based on the information theory and from the viewpoint of optimal information on description—...Gauss-Markov model is frequently used in data analysis;the analysis and estimation of its parameters is always a hot issue.Based on the information theory and from the viewpoint of optimal information on description—minimum description length,this paper discusses a case:where there is multi-collinearity in the coefficient matrix,principal component estimation is used to estimate and select the original parameters,so as to reduce its multi-collinearity and improve its credibility.From the viewpoint of minimum description length,this paper discusses the approach of selecting principal components and uses this approach to solve a practical problem.展开更多
For the two seemingly unrelated regression system, this paper proposed a new type of estimator called pre-test principal components estimator (PTPCE) and discussed some properties of PTPCE.
In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias es...In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.展开更多
Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in- cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To...Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in- cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal component analysis. In this approach, mutual information estimation and Bayesian information criterion （BIC） are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation （BP） network is applied whose input is multivar- iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis （LKPCA） model for incipient fault prognosis. The new method has been exemplified in a sim- ple nonlinear process and the complicated Tennessee Eastman （TE） benchmark process. The results indicate that the new method has suoerioritv in the fault prognosis sensitivity over other traditional fault prognosis methods.展开更多
Outlier mining is an important aspect in data mining and the outlier miningbased on Cook distance is most commonly used. But we know that when the data have multicollinearity,the traditional Cook method is no longer e...Outlier mining is an important aspect in data mining and the outlier miningbased on Cook distance is most commonly used. But we know that when the data have multicollinearity,the traditional Cook method is no longer effective. Considering the excellence of the principalcomponent estimation, we use it to substitute the least squares estimation, and then give the Cookdistance measurement based on principal component estimation, which can be used in outlier mining.At the same time, we have done some research on related theories and application problems.展开更多
文摘The article deals with optimality of combining ridge and principal component estimator.It is proved that combining ridge and principal componet estimate has several types of minimumvariance properties in the class of reduced dimension estimates and it also has minimum of orthogo-nal unchanged norm of covariance in the same class.
基金Project(40074001)supported by National Natural Science Foundation of ChinaProject(SD2003-10)supported by the Open ResearchFund Programof the Key Laboratory of Geomatics and Digital Technilogy,Shandong Province
文摘Gauss-Markov model is frequently used in data analysis;the analysis and estimation of its parameters is always a hot issue.Based on the information theory and from the viewpoint of optimal information on description—minimum description length,this paper discusses a case:where there is multi-collinearity in the coefficient matrix,principal component estimation is used to estimate and select the original parameters,so as to reduce its multi-collinearity and improve its credibility.From the viewpoint of minimum description length,this paper discusses the approach of selecting principal components and uses this approach to solve a practical problem.
文摘For the two seemingly unrelated regression system, this paper proposed a new type of estimator called pre-test principal components estimator (PTPCE) and discussed some properties of PTPCE.
文摘In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.
基金Supported by the National Natural Science Foundation of China(61573051,61472021)the Natural Science Foundation of Beijing(4142039)+1 种基金Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2015KF-01)Fundamental Research Funds for the Central Universities(PT1613-05)
文摘Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in- cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal component analysis. In this approach, mutual information estimation and Bayesian information criterion （BIC） are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation （BP） network is applied whose input is multivar- iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis （LKPCA） model for incipient fault prognosis. The new method has been exemplified in a sim- ple nonlinear process and the complicated Tennessee Eastman （TE） benchmark process. The results indicate that the new method has suoerioritv in the fault prognosis sensitivity over other traditional fault prognosis methods.
文摘Outlier mining is an important aspect in data mining and the outlier miningbased on Cook distance is most commonly used. But we know that when the data have multicollinearity,the traditional Cook method is no longer effective. Considering the excellence of the principalcomponent estimation, we use it to substitute the least squares estimation, and then give the Cookdistance measurement based on principal component estimation, which can be used in outlier mining.At the same time, we have done some research on related theories and application problems.
