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
Binary sensor network(BSN) are becoming more attractive due to the low cost deployment,small size,low energy consumption and simple operation.There are two different ways for target tracking in BSN,the weighted algori...Binary sensor network(BSN) are becoming more attractive due to the low cost deployment,small size,low energy consumption and simple operation.There are two different ways for target tracking in BSN,the weighted algorithms and particle filtering algorithm.The weighted algorithms have good realtime property,however have poor estimation property and some of them does not suit for target’s variable velocity model.The particle filtering algorithm can estimate target's position more accurately with poor realtime property and is not suitable for target’s constant velocity model.In this paper distance weight is adopted to estimate the target’s position,which is different from the existing distance weight in other papers.On the analysis of principle of distance weight (DW),prediction-based distance weighted(PDW) algorithm for target tracking in BSN is proposed.Simulation results proved PDW fits for target's constant and variable velocity models with accurate estimation and good realtime property.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This work is supported by The National Science Fund for Distinguished Young Scholars （60725105） National Basic Research Program of China （973 Program） （2009CB320404）+5 种基金 Program for Changjiang Scholars and Innovative Research Team in University （IRT0852） The National Natural Science Foundation of China （60972048, 61072068） The Special Fund of State Key Laboratory （ISN01080301） The Major program of National Science and Technology （2009ZX03007- 004） Supported by the 111 Project （B08038） The Key Project of Chinese Ministry of Education （107103）.
文摘Binary sensor network(BSN) are becoming more attractive due to the low cost deployment,small size,low energy consumption and simple operation.There are two different ways for target tracking in BSN,the weighted algorithms and particle filtering algorithm.The weighted algorithms have good realtime property,however have poor estimation property and some of them does not suit for target’s variable velocity model.The particle filtering algorithm can estimate target's position more accurately with poor realtime property and is not suitable for target’s constant velocity model.In this paper distance weight is adopted to estimate the target’s position,which is different from the existing distance weight in other papers.On the analysis of principle of distance weight (DW),prediction-based distance weighted(PDW) algorithm for target tracking in BSN is proposed.Simulation results proved PDW fits for target's constant and variable velocity models with accurate estimation and good realtime property.
