Generalized multivariate ridge regression estimate and criteria q(c) for choosing matrixK |
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Authors: | Chen Shi-ji Zeng Zhi-bin |
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Institution: | 1. Department of Mathematics, Fujian Normal University, Fuzhou;2. Statistics Bureau of Fujian Province. Fuzhou |
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Abstract: | When multicollinearity is present in a set of the regression variables, the least square estimate of the regression coefficient
tends to be unstable and it may lead to erroneous inference.
In this paper, generalized ridge estimate β(K) of the regression coefficient β =vec(B) is considered in multivaiate linear
regression model. The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter
matrix K. Moreover, it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several
weaknesses. In order to overcome these weaknesses, a new family of criteria Q(c) is adpoted which includes the criterion MSE
and criterion LS as its special case. The good properties of the criteria Q(c) are proved and discussed from theoretical point
of view. The statistical meaning of the scale c is explained and the methods of determining c are also given.
The projects Supported by Natural Science Foundation of Fujian Province |
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Keywords: | least square estimate generalized ridge estimate mean square error |
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