THE EXPECTED VALUES OF INVARIANT POLYNOMIALS WITH MATRIX ARGUMENT OF ELLIPTICAL DISTRIBUTIONS  

作　　者：李润泽 

出　　处：《Acta Mathematicae Applicatae Sinica》1997年第1期64-70,共6页应用数学学报（英文版）

摘　　要：Invariant polynomials with matrix arguments have been defined by the theory of group representation, 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 interesting polynomials has been shown by people working in the field of econometric theory. In this paper. we derive the expected values of C (BR.BU). Ck (BR)C (BU) and Ck (B-1U), where Bd＝X′X and Xnxp is distributed according to an elliptical matrix distribution. We also give their applications in multivariate distribution theory including the related development in econometrics.Invariant polynomials with matrix arguments have been defined by the theory of group representation, 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 interesting polynomials has been shown by people working in the field of econometric theory. In this paper. we derive the expected values of C (BR.BU). Ck (BR)C (BU) and Ck (B-1U), where Bd＝X′X and Xnxp is distributed according to an elliptical matrix distribution. We also give their applications in multivariate distribution theory including the related development in econometrics.

关 键 词：Elliptical matrix distributions invariant polynomials zonal polynomials 

分 类 号：O174[理学—数学]