Scatter plots for two multivariate normal data sets may suggest that the constant-density ellipsoid contours of underlying density functions have the same directions. In other words, covariance matrices of the two populations have the same eigenvectors matrix in their spectral decomposition...

AMS classifications: 60F05, 62G09; 62G20.

Let {Vn; n = 1} be a sequence of random elements in a separable normed linear space E, uniformly dominated by a random variable V. Let {Ank; K = 1, 2, ..., n; n = 1} be a triangular array of random variables. In this paper, conditions for the convergence of [Sigma]k=1n AnkVk to zero (in...

If a sequence of random variables Xn converges to X in probability we know little about the pointwise behavior Xn([omega]). In this note we show that if Xn converges to X quickly enough (for example, like n-[alpha] for [alpha] 0) then, for almost all [omega], Xn([omega]) converges to X([omega])...