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
a linear model,be the LS estimate ofDenote by u, the (1,1) -element ofAssume that Eet=0 and {ei} obeys theGauss-Markov conditionIt is shown thatis a sufficient condition forto be strongly consistent. This condition is...a linear model,be the LS estimate ofDenote by u, the (1,1) -element ofAssume that Eet=0 and {ei} obeys theGauss-Markov conditionIt is shown thatis a sufficient condition forto be strongly consistent. This condition is accurate in the sense that for any0, the conditionceases to be sufficient. Some remarks are made concerning the necessary and/orsufficient condition for to be strongly consistent.展开更多
The present paper deals with the inefficiency of the least square estimates in linear models.FOr Gauss-Markov model, a new efficiency is proposed and its lower bound is given. FOr variancecomponent model, an efficienc...The present paper deals with the inefficiency of the least square estimates in linear models.FOr Gauss-Markov model, a new efficiency is proposed and its lower bound is given. FOr variancecomponent model, an efficiency is introduced and its lower bound, which is independent ofunknown parameters, is obtained.展开更多
基金Project(40074001) supported by National Natural Science Foundation of China Project (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.
基金supported by the Natural Science Foundation of Jiangxi Province(20144BAB2110001)Humanities and Social Science Planning Foundation in College of Jiangxi Province(TJ1401)the National Social Science Foundation of China(12BTJ014)
基金Project supported by the National Natural Science Foundation of China.
文摘a linear model,be the LS estimate ofDenote by u, the (1,1) -element ofAssume that Eet=0 and {ei} obeys theGauss-Markov conditionIt is shown thatis a sufficient condition forto be strongly consistent. This condition is accurate in the sense that for any0, the conditionceases to be sufficient. Some remarks are made concerning the necessary and/orsufficient condition for to be strongly consistent.
文摘The present paper deals with the inefficiency of the least square estimates in linear models.FOr Gauss-Markov model, a new efficiency is proposed and its lower bound is given. FOr variancecomponent model, an efficiency is introduced and its lower bound, which is independent ofunknown parameters, is obtained.
