In this paper the distribution of the sum of independent[Gamma]variables with different scale parameters is obtained by direct integration, without involving a series expansion. One of its particular cases is the distribution of the product of some particular independent Beta variables. Both...

LetAbe annbynmatrix whose elements are independent random variables with standard normal distributions. Girko's (more general) circular law states that the distribution of appropriately normalized eigenvalues is asymptotically uniform in the unit disk in the complex plane. We derive the exact...

In this paper, a general form ofM-estimation is proposed and some asymptotics are investigated. The model covers all linear and nonlinear regression models, AR time series, EIVR models, etc. as its special cases. The dispersion functions may be convex or differences of convex functions, the...

Hart and Vieu proposed a modified cross validation (MCV), the "leave-(2l+1)-out" version of the simple cross validation for bandwidth selection under dependence and established its asymptotic optimality for a certain class ofl. In this article, we investigate the convergence rates of MCV.

In this paper we obtain an asymptotic expansion for the distribution of Hotelling'sT2-statisticT2under nonnormality when the sample size is large. In the derivation we find an explicit Edgeworth expansion of the multivariatet-statistic. Our method is to use the Edgeworth expansion and to expand...

Considering a large class of tests, we study higher order power in a possibly non-iid set-up. Optimum properties for the likelihood ratio and score tests are exhibited under the criteria of second-order local maximinity and third-order local average power, respectively. The issue of stringency...

Jamison's classification of scalar stationary Gaussian reciprocal processes is extended to multivariate Gaussian reciprocal diffusions (GRDs). The second-order self-adjoint differential equation satisfied by the covariance of a GRD specifies a Hamiltonian matrix whose eigenstructure is employed...

In canonical correlation analysis the number of nonzero population correlation coefficients is called the dimensionality. Asymptotic distributions of the dimensionalities estimated by Mallows's criterion and Akaike's criterion are given for nonnormal multivariate populations with finite fourth...

In this paper we develop, for directional and axial data, smooth tests of goodness-of-fit for rotationally symmetric distributions against general families of embedding alternatives constructed from complete orthonormal bases of functions. These families generalize a proposal of Beran (1979)...

The paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by[sigma]-finite measures and parametrized by vector-valued variables. It introduces[phi]-divergence testing statistics as alternatives to the classical ones:...