In this paper, we present both integral and infinite series expressions of μqp≡E[(x′Ax)p/(x′Bx)q] when x∼N(μ,In), where p, q are nonnegative real numbers, A is a symmetric matrix, and B is a positive semi-definite matrix. We also present efficient numerical methods for computing μqp...

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of...

We provide a feasible generalized least squares estimator for (unrestricted) multivariate GARCH(1, 1) models. We show that the estimator is consistent and asymptotically normally distributed under mild assumptions. Unlike the (quasi) maximum likelihood method, the feasible GLS is considerably...

We study properties of Fisher distribution (von Mises–Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011) [16], and a method of series expansion for evaluating the...

Pollard showed for k-means clustering and a very broad class of sampling distributions that the optimal cluster means converge to the solution of the related population criterion as the size of the data set increases. We extend this consistency result to k-parameters clustering, a method derived...

Let the kp-variate random vector X be partitioned into k subvectors Xi of dimension p each, and let the covariance matrix [Psi] of X be partitioned analogously into submatrices [Psi]ij. The common principal component (CPC) model for dependent random vectors assumes the existence of an orthogonal...