Showing papers by "Runze Li published in 1997"
TL;DR: In this article, some probability plots are proposed to test spherical and elliptical symmetry in terms of some invariant statistics under orthogonal transformations, and the empirical percentiles of these correlation coefficients are calculated by simulation.
Abstract: This article proposes some probability plots are proposed to test spherical and elliptical symmetry in terms of some invariant statistics under orthogonal transformations. Some correlation coefficients as numerical measures of detecting deviation from spherical or elliptical symmetry are recommended, and the empirical percentiles of these correlation coefficients are calculated by simulation. The simulation results for data sets from 12 different populations show that the new plots are useful for testing spherical and elliptical symmetry. Some discussion is given also.
51 citations
TL;DR: Two methods for generating both an NT-net and the uniform distribution on a Stiefel manifold O(n,m), where O( n,m) = {bdH:H is an n×m matrix and H′H = Im}.
20 citations
TL;DR: In this paper, the expected values of invariant polynomials with matrix arguments have been derived in terms of the power series of group representation, generalizing the zonal polynomial.
Abstract: 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 ofC φ κ,λ (BR,BU),Cκ(BR)Cλ(BU) andCκ(B−1U), whereBB d =X′X andXn×p is distributed according to an elliptical matrix distribution. We also give their applications in multivariate distribution theory including the related development in econometrics.
10 citations