On the singularity of multivariate skew-symmetric models (Q968495)

Using a colloquial style and awkward notation, the authors first solve the problem of characterizing the symmetric kernels leading to singular Fisher information matrices in the vicinity of symmetry for a class of multivariate skew-symmetric distributions. Then they show that in broad classes of semiparametric skew-symmetric distributions, the only kernels leading, for any sample of size \(n\geq3\) and in the vicinity of symmetry, to a stationary point of the profile log-likelihood function for skewness are the normal ones.