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特征函数的函数形式与多元分布刻画AI 解读

During the Oxford Conference of the Econometric Society in 1936, Ragnar Frisch proposed a problem of characterization of distributions based on the property of linear regression of one linear function of random variables on the other. This problem has been solved, partially by Allen [1], and then completely by Rao [24,25], Fix [7], and Laha [13] relaxing the conditions imposed on the component random variables. The purpose of this paper is to solve the above mentioned…

最高阶不变多项式的构造方法AI 解读

The invariant polynomials (Davis [8] and Chikuse [2] with r ( r ≥ 2) symmetric matrix arguments have been defined, extending the zonal polynomials, and applied in multivariate distribution theory. The usefulness of the polynomials has attracted the attention of econometricians, and some recent papers have applied the methods to distribution theory in econometrics (e.g., Hillier [14] and Phillips [22]). The ‘top order’ invariant polynomials , in which each of the partitions…

矩阵变量不变多项式及其在计量分布理论中的应用综述AI 解读

Invariant polynomials with matrix arguments have been defined by the theory of group representations, generalizing the zonal polynomials. They have developed as a useful tool to evaluate certain integrals arising in multivariate distribution theory, which were expanded as power series in terms of the invariant polynomials. Some interest in the polynomials has been shown by people working in the field of econometric theory. In this paper, we shall survey the properties of the…

多元 Behrens–Fisher 判别分析中的矩阵变量与特征根分布AI 解读

In this paper it is shown that some distributions of the matrix variates and latent roots arising in the multivariate Behrens-Fisher discriminant problem can be explicitly expressed in terms of the invariant polynomials with two matrix arguments, due to A. W. Davis, extending the zonal polynomials of matrix argument.