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When a (p+q)-variate column vector (x′,y′)′ has a (p+q)-variate normal density with mean vector (μ1,μ2) and covariance matrix Ω, unknown, Schervish (1980) obtains prediction intervals for the linear functions of a future y,
given x. He bases the prediction interval on the F-distribution. However, for a specified linear function the statistic to
be used is Student's t, since the prediction intervals based on t are shorter than those based on F. Similar results hold
for the multivariate linear regression model. 相似文献
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D. G. Kabe 《Australian & New Zealand Journal of Statistics》1968,10(1):21-23
In this paper we generalize a result of Kshirsagar's (1960, pp. 83–84) on the distribution of the regression coefficient matrix for a multivariate normal population. 相似文献
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D. G. Kabe 《统计学通讯:理论与方法》2013,42(20):2571-2581
Subbaiah and Mudhol kar (1978) remark the general mu1tivariate linear hypothesis testing step down procedure statistics do not appear to be maximal invariants under nonsingular lower triangular matrix transformations of the original variates. This paper proves the maximal invariance of these statistics. The invariance results are essential to study the power functions of the step down procedures for MANOVA problems. An example is given to show that such power function studies are very involved. 相似文献
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In this paper two tests for testing the hypothesis that the stochastic endogenous regressors in a structural equation, embedded in a system of simultaneous structural equations, are independent of the disturbances in that equation are presented. 相似文献
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D.G. Kabe 《统计学通讯:理论与方法》2013,42(11):3419-3427
For the generalized MANOVA (GMANOVA) model of Potthoff and Roy (1964), X = BξA + E, Khatri (1966) derives the likelihood ratio test criterion for test-ing the composite double linear null hypothesis CξV = 0, C,V known. This criterion plays an important role in statistics, and several authors have recently studied its further properties. However, Khatri's (1966) de-reviation of the distribution of this criterion is involved. By noting that the GMANOVA model is re-stricted MANOVA model, this paper presents an alter-native simple derivation of the distribution of this criterion. The derivation is based on the generalized Sverdrup's lemma, Kabe (1965). 相似文献
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D.G. Kabe 《统计学通讯:理论与方法》2013,42(24):2545-2550
Given the usual normal multivariate linear regression model Y = BX + E, with B subjected to double linear restrictions GBF' = T, a likelihood ratio test criterion for testing the composite linear null hypothesis HBJ' = U; G, F, T, H, J, U specified, is provided. The applications of such tests are discussed by Timm (1980). 相似文献
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Two Route first-cluster second vehicle routing algorithms are contrasted in the first section of the paper. Next, the ‘large’ number of feasible solutions to a multiple travelling salesman problem is established given that each salesman can visit any number of customers in a stated range. An approximate expression is given for the ‘small’ fraction of this solution space searched by a route first-cluster second vehicle routing heuristic. Nevertheless, this heuristic is seen to be a very efficient means of searching its solution space. 相似文献