This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably...

Let X,X1,...,Xm,..., Y,Y1,...,Yn,... be independent d-dimensional random vectors, where the Xj are i.i.d. copies of X, and the Yk are i.i.d. copies of Y. We study a class of consistent tests for the hypothesis that Y has the same distribution as X+[mu] for some unspecified . The test statistic L...

Goodness-of-fit and symmetry tests are proposed for the innovation distribution in generalized autoregressive conditionally heteroscedastic models. The tests utilize an integrated distance involving the empirical characteristic function (or the empirical Laplace transform) computed from properly...

Although still being recommended as a goodness-of-fit test for normality, we present some motivations to consider D'Agostino's statistic D for testing of uniformity on an unknown interval. As a matter of fact, D turns out to be a linear function of the Cramer-von Mises distance between the...

We derive the asymptotic distributions for measures of multivariate skewness and kurtosis defined by Malkovich and Afifi if the underlying distribution is elliptically symmetric. A key step in the derivation is an approximation by suitable Gaussian processes defined on the surface of the unit...

Let Dn,r denote the largest rth nearest neighbor link for n points drawn independently and uniformly from the unit d-cube Cd. We show that according as r < d or r>d, the limiting behavior of Dn,r, as n -- [infinity], is determined by the two-dimensional 'faces' respectively one-dimensional 'edges' of the...</d>

We propose a new weighted integral goodness-of-fit statistic for exponentiality. The statistic is motivated by a characterization of the exponential distribution via the mean residual life function. Its limit null distribution is the same as that of a certain weighted integral of the squared...