Sufficient conditions are given that certain statistics have a common distribution under a wide class of underlying distributions. Invariance methods are the primary technical tool in establishing the theoretical results. These results are applied to MANOVA problems, problems involving canonical...

The speed of convergence in the functional central limit theorem (or invariance principle) for partial sum processes based on real-valued functions of Markov processes satisfying Doeblin's condition is studied where Prokhorov's metric is used to measure the distance between probability...

A robust estimator of the regression function is proposed combining kernel methods as introduced for density estimation and robust location estimation techniques. Weak and strong consistency and asymptotic normality are shown under mild conditions on the kernel sequence. The asymptotic variance...

. Let Xn, n = 1, be a sequence of tight random elements taking values in a separable Banach space B such that Xn, n = 1, is uniformly integrable. Let ank, n = 1, k = 1, be a double array of real numbers satisfying [Sigma]k = 1 ank <= [Gamma] for every n >= 1 for some positive constant [Gamma]. Then [Sigma]k = 1 ankXk,...</=>

The regularity of trajectories of continuous parameter process (Xt)t[set membership, variant]R+ in terms of the convergence of sequence E(XTn) for monotone sequences (Tn) of stopping times is investigated. The following result for the discrete parameter case generalizes the convergence theorems...

The properties of N-Hida processes Part 1 ([6.], J. Multivar. Anal. 15, 336-360) are studied when the indices set is 2. First, the past of a point (s, t) of 2 is extended to st = [sigma]{[gamma]uv, u = s or v = t}. The dimension of the linear space generated by the conditional expectations of an...

Let [Omega] = {1, 0} and for each integer n = 1 let [Omega]n = [Omega] - [Omega] - ... - [Omega] (n-tuple) and [Omega]nk = {(a1, a2, ..., an)(a1, a2, ... , an) [epsilon] [Omega]n and [Sigma]i=1nai = k} for all k = 0,1,...,n. Let {Ym}m=1 be a sequence of i.i.d. random variables such that . For...

A number of algorithms are presented for calculating the exact likelihood of a multivariate ARMA model. There are two aspects to the algorithms. Firstly, the parameterization is in terms of AR parameters and autocovariances. This obviates difficulties with initial MA estimates. Secondly, the...

Let X1,..., Xp be p (= 3) independent random variables, where each Xi has a distribution belonging to the one-parameter exponential family of distributions. The problem is to estimate the unknown parameters simultaneously in the presence of extreme observations. C. Stein (Ann. Statist. 9 (1981),...

Scalar polynomial statistics are found which have constant regression on the mean of a sample of Wishart matrices. The method used is to differentiate the characteristic function associated with the Wishart distribution, thus expressing the constant regression condition as a differential...