In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
Given the limitation of traditional univariate analysis method in processing the multicollinearity of dam monitoring data,this paper reconstructs the multivariate response variables by introducing principal component ...Given the limitation of traditional univariate analysis method in processing the multicollinearity of dam monitoring data,this paper reconstructs the multivariate response variables by introducing principal component analysis(PCA)method,explores the ways of determining principal components(PCs),and extracts a few PCs that have major influence on data variance.For steady observation series,a control field for the whole observation values has been established based upon PCA;for unsteady observation series that have significant tendency,a control field for the future observation values has been constructed according to PC statistical predication model.These methods have already been applied to an actual project and the results showed that data interpretation method with PCA can not only realize data reduction,lower data redundancy,and reduce noise and false alarm rate,but also be effective to data analysis,having a broad application prospect.展开更多
The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parame...The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.展开更多
文摘In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
基金supported by the National Natural Science Foundation of China(Grant Nos 50909041,50879024,50809025,50539010,50539110)the National Supporting Program(Grant Nos 2008BAB29B03,2008BAB-29B06)the Natural Science Foundation of Hohai University(Grant No 2008426811)
文摘Given the limitation of traditional univariate analysis method in processing the multicollinearity of dam monitoring data,this paper reconstructs the multivariate response variables by introducing principal component analysis(PCA)method,explores the ways of determining principal components(PCs),and extracts a few PCs that have major influence on data variance.For steady observation series,a control field for the whole observation values has been established based upon PCA;for unsteady observation series that have significant tendency,a control field for the future observation values has been constructed according to PC statistical predication model.These methods have already been applied to an actual project and the results showed that data interpretation method with PCA can not only realize data reduction,lower data redundancy,and reduce noise and false alarm rate,but also be effective to data analysis,having a broad application prospect.
基金supported by the Natural Science Foundation of China under Grant Nos.10771017 and 11071022Key Project of MOE,PRC under Grant No.309007
文摘The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.
