We develop a theory of asymptotics for Rényi-type weighted empirical and quantile processes and statistics via characterising their possible limiting behaviour in the middle and on the tails. In case of moderate weight functions tail limiting behaviour is found to be Gaussian, while heavily...

Let X = {X(t), -[infinity]t[infinity]} be a continuous-time stationary process with spectral density [phi]X([lambda]; [theta]), where [theta] is a vector of unknown parameters. Let {[tau]k} be a stationary point process on the real line which is independent of X. The identifiability and the...

A good robust functional should, if possible, be efficient at the model, smooth, and have a high breakdown point. M-estimators can be made efficient and Fréchet differentiable by choosing appropriate [psi]-functions but they have a breakdown point of at most 1/(p + 1) in p dimensions. On the...

A system of particles of k types in Rd is considered, where each particle, depending on its type, migrates and lives a random amount of time, at the end of which it branches according to a multitype law. The demographic variation process is a non-Markovian process which measures the changes in...

For a generalized normal linear model in which the covariance matrix [Sigma] is positive definite symmetric, UMP invariant test procedures for some kinds of linear hypotheses are derived by transforming the model by an orthogonal matrix L, consisting of orthonormal eigenvectors of [Sigma] as the...

Our goal is to demonstrate on n the Holley, Kusuoka, and Stroock result about the asymptotic behavior of the second eigenvalue associated to dynamical systems with a small random perturbation.

We give necessary and sufficient conditions for the linearity of multiple regression on a general stable vector, along with a sufficient condition for the finiteness of the conditional absolute moment when 0 < [alpha] <= 1.

Subclasses [beta](E), -2 < [beta] <= -1, of the Lévy class L of self-decomposable measures on a Banach space E are examined. They are closed convolution subsemigroups of the semigroup of infinitely divisible probability distributions on E, defined as limit distributions of some prescribed schemes of summation. Each element of [beta](E) belongs to the domain of normal attraction of a stable measure with exponent -[beta]. Their Fourier transforms are characterized. The symmetric measures in [beta](E) are shown to decompose uniquely into the convolution product of a symmetric stable measure with exponent -[beta] and the probability distribution of a random integral of the form [integral operator](0,1) t dY(t[beta]), where Y is a Lévy process with paths in the Skorohod space DE[0, [infinity]) and Y(1) has finite (-[beta])-moment. Topological and algebraic properties of the random-integral mapping [beta]: (Y(1)) --> [[integral operator](0,1) t dY(t[beta])] are investigated when E is a Hilbert space. As an application of the fact that [beta] is a continuous isomorphism, generators for [beta] are found as the images of compound Poisson distributions. Finally, the connection between...</[beta]>

Let B be a real separable Banach space with norm ßB, X, X1, X2, ... be a sequence of centered independent identically distributed random variables taking values in B. Let sn = sn(t), 0 <= t <= 1 be the random broken line such that sn(0) = 0, sn(k/n) = n-1/2 [Sigma]i=1k Xi for n = 1, 2, ... and k = 1, ..., n. Denote snB = sup0 <= t <= 1 sn(t)B and assume that w(t), 0 <= t <= 1 is the Wiener process such that covariances of w(1) and X are equal. We show that under appropriate conditions P(snB > r) = P(wB r)(1 + o(1)) and give estimates of the remainder term. The results are new already in the case of...</=>

It is shown that the traditional estimator of a discriminant coefficient vector is the generalized Bayes estimator with respect to a prior which can be approximated by proper priors. As a corollary the admissibility of this procedure in the class of all scale equivariant estimators is derived.