In this paper we investigate the dimensional structure of probability distributions on Euclidean space and characterize a class of regular distributions. We obtain a consistent estimator of dimension based on a nearest neighbor statistic and in addition obtain asymptotic confidence intervals for...

The problem of the characterization of multivariate distribution through the property of the zero regression of linear statistic on another one was posed by C. R. Rao. The characterization of probability distributions with independent operator-semistable components by this property is given.

A semimartingale driven continuous time linear regression model is studied. Assumptions concerning errors allow us to consider also models with infinite variance. The order of the almost sure convergence of a class of estimates which includes least squares estimates is given. In the presence of...

Let (X1, Y1),..., (Xn, Yn) be i.i.d. rv's and let m(x) = E(YX = x) be the regression curve of Y on X. A M-smoother mn(x) is a robust, nonlinear estimator of m(x), defined in analogy to robust M-estimators of location. In this paper the asymptotic maximal deviation sup0 = t = 1 mn(t) - m(t) is...

Let X = [sigma]Z be a scale mixture of a random variable with the scale factor [sigma]. In this paper we consider the expansions G[sigma], k(x) = [Sigma]k - 1j = 0 (j!)-1 a[sigma], j(x) E([sigma][sigma] -1)j as approximations for the distribution function F(x) of X, where [delta] = 1 or -1, k is...

Given a p-dimensional spectral density [phi]([omega])=cI0, [for all][omega][set membership, variant][0,2[pi]] such that [phi]r([omega]) [set membership, variant] Lip* ([alpha]), with covariance block-Toeplitz matrix [Gamma]n of dimension np - np, we show that b=(r+[alpha])/(1+r+[alpha]),...

The weak convergences of U- and V-statistics were established by Yoshihara (1976, Z. Warsch. Verw. Gebiete 35 237-252) for stationary absolutely regular processes. Later Yoshihara (1978, Z. Warsch. Verw. Gebiete 43 101-127) also proved the weak convergence of one sample rank order statistics...

This paper concerns an asymptotic expansion for the distribution of the sum of independent zero-one random variables in case where this surn has variance [sigma]n2 -- [infinity]. The expansion presented is given to the order O([sigma]n-2). An application to the study of the exact rate of...

Let F(s, t) = P(X s, Y t) be the bivariate survival function which is subject to random censoring. Let be the bivariate product limit estimator (PL-estimator) by Campbell and Földes (1982, Proceedings International Colloquium on Non-parametric Statistical Inference, Budapest 1980,...