We consider the problem of testing uniformity on high-dimensional unit spheres. We are primarily interested in nonnull issues. We show that rotationally symmetric alternatives lead to two Local Asymptotic Normality (LAN) structures. The first one is for fixed modal location θ and allows to derive locally asymptotically most powerful tests under specified θ . The second one, that addresses the F...

Professor Bai's contributions to Edgeworth Expansions are reviewed. Author's collaborations with Professor Bai on the topic are also discussed. I have the pleasure of collaborating with Professor Bai Zhidong on many papers including three [2–4] on Edgeworth expansions. The earliest work of Bai on Edgeworth expansions that I came across is the English translation [10] of his joint work with Lin ...

n of a fixed state ρ, the joint state converges to a displaced thermal equilibrium state of a quantum harmonic oscillator. The precise meaning of the convergence is that there exist physical transformations Tn (trace preserving quantum channels) which map the qubits states asymptotically close to their corresponding oscillator state, uniformly over all states in the local neighborhood. A few co...

Many multivariate statistical methods call upon the assumption of multivariate normality. However, many researchers fail to test this assumption. This omission could be due either to ignorance of the existence of tests of multivariate normality or confusion about which test to use. Although at least 50 tests of multivariate normality exist, relatively little is known about the power of these pr...

Reference values seem crucial to both veterinary medicine and human medicine. The main critique is that the theoretical connections between the concepts of reference values, normality, and health are weak. In this paper, we analyze especially one attempt in veterinary medicine to establish such a theoretical connection. We find that this attempt fails because it is circular. In conclusion, we w...