排序方式: 共有11条查询结果,搜索用时 15 毫秒
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Simplified proofs are given of a standard result that establishes positive semi–definiteness of the difference of the inverses of two non–singular matrices, and of the extension of this result by Milliken and Akdeniz (1977) to the difference of the Moore–Penrose inverse of two singular matrices. 相似文献
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Dale Borowiak 《统计学通讯:理论与方法》2013,42(24):2911-2921
The case of selecting between a set of fixed models is considered. The true model is assumed to be contained in the set of proposed models and errors are taken to be normally distributed. A sequential procedure which yeilds probabilities of incorrect selections is proposed. The procedure is shown to have optimal properties and is extended to the estimated model case by a bootstrap procedure. 相似文献
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The construction of kernel discriminant coordinates reduces to the solution of a generalized eigenvalue problem in which both matrices are nonnegative definite. Six different algorithms for solving that problem are described, and the performance of these algorithms is tested on 26 different datasets. The percentage of misclassifications using a linear discriminant function is noted, and the algorithms’ running times are ascertained. Classification is also performed in the space of classical discriminant coordinates. 相似文献
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《统计学通讯:理论与方法》2012,41(13-14):2588-2601
In the investigation of the restricted linear model ? r = {y, X β | A β = b, σ2 Σ}, the parameter constraints A β = b are often handled by transforming the model into certain implicitly restricted model. Any estimation derived from the explicitly and implicitly restricted models on the vector β and its functions should be equivalent, although the expressions of the estimation under the two models may be different. However, people more likely want to directly compare different expressions of estimations and yield a conclusion on their equivalence by using some algebraic operations on expressions of estimations. In this article, we give some results on equivalence of the well-known OLSEs and BLUEs under the explicitly and implicitly restricted linear models by using some expansion formulas for ranks of matrices. 相似文献
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矩阵双加权广义逆的Zlobec型公式 总被引:1,自引:0,他引:1
本文提出了双加权广义逆的概念,将常用的四种加权广义逆统一为一种形式,并依据加权广义逆矩阵的Zlobec型公式得到了双加权广义逆矩阵的Zlobec型公式. 相似文献
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If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is to be used as a tool for analysing abstract, uninhabited decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x less powerful than y when measured in the simple voting game G1 , but more powerful than y when G1 is bicamerally joined with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power). 相似文献
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《统计学通讯:理论与方法》2012,41(16-17):2983-2990
Assessing the goodness-of-fit of latent variable models for categorical data becomes a problem in presence of sparse data since the classical goodness-of-fit statistics are badly approximated by the chi square distribution. A good solution to this problem is represented by statistical tests based on the residuals associated to marginal distributions of the manifest variables (Cagnone and Mignani, 2007; Maydeu-Olivares and Joe, 2005; Reiser, 1996). The quadratic form associated to the test involves the use of a generalized inverse of the covariance matrix of the sample proportions. In this article we prove that the rank of the Moore-Penrose generalized inverse is univocally determined and hence it can be used appropriately. 相似文献
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研究相对于M和N的加权Moore-Penrose逆,得到带有对合反自同构的有单位元的结合环R上的一类可分解矩阵的加权Moore-Penrose逆存在的充分必要条件.当M和N为单位矩阵时,相对于M和N的加权Moore-Penrose逆就是大家熟悉的Moore-Penrose逆.从某种意义上说,相对于M和N的加权Moore-Penrose逆也是相对于M和N的广义Moore- Penrose逆的推广.结论一方面可特殊化到Moore-Penrose逆的情形,另一方面可得到有关A相对于M和N的广义Moore- Penrose逆的结论. 相似文献
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