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有限总体抽样中乘积矩的期望与估计AI 解读

This article presents improvements in and an extension of results published in this journal by Nath in 1968 and 1969 and by Raghunandanan and Srinivasan in 1973 for two general multivariate expectation problems and a related estimation problem. Our presentation applies a modification of basic theory developed by H.C. Carver and his students at the University of Michigan in the 1930's and gives more compact and adequate solutions to the expectation problems. Using related and…

利用矩阵导数判定多元极大值与极小值AI 解读

The purpose of this paper is the presentation of formulae for obtaining matrix derivatives of the second order to use in making tests for maxima and minima. The theory of such second order derivatives is presented. These formulae require the rearrangment of the parameter elements in vector form and the transformed results feature Kronecker products, which have certain desirable properties. Application is made to several types of problems.