Let {Xj}j = - [infinity][infinity] be a vector-valued stationary process with a first-order univariate probability density f on Rd. We consider the recursive estimation of f(x) from n observations {Xj}j=1n which need not be independent. For processes {Xj}j = - [infinity][infinity] which are...

A central limit theorem for a class of non-instantaneous filters of a stationary Gaussian process is proved and it is applied to study the limiting distributions of the number of zero-crossings.

We describe a class of smoothed orthogonal series density estimates, including the classical sequential-series introduced by [6], Soviet Math. Dokl. 3 1559-1562) and [16], Ann. Math. Statist. 38 1261-1265), and [23], Ann. Statist 9 146-156) two-parameter smoothing. The Bowman-Rudemo method of...

This paper propounds a short proof of a result previously proved by F. Knight and P. A. Meyer (1976, Z. Warsch. Verw. Gebiete 34 129-134). Let X be a random variable in n with the following property: for any matrix (ca bb) in GL(n+1) (where a is a (n, n) matrix) there exist [alpha] in GL(n) and...

The classical point estimation problem is investigated under alternative loss functions which are quasi-convex and symmetric with respect to some subgroup of the orthogonal group in n. A characterization of better estimators is proved and applied to scale and translation families of estimators....

Asymptotic independence under weak convergence of sequences of bivariate random vectors is studied via the behavior of a certain class of bivariate cdf iterands that includes the extreme value iterand and a certain maximin iterand.

Sufficient conditions are found for the weak convergence of a weighted empirical process {([nu]n(C)/q(P(C))) 1 [P(C) [succeeds, curly equals] [lambda]n]: C [set membership, variant] }, indexed by a class of sets and weighted by a function q of the size of each set. We find those functions q...

Under the errors-in-variables parameterization, the limiting behavior of the estimators of the parameters of the factor analysis model is investigated. An explicit expression is given for the covariance matrix of the limiting distribution of the estimators. It is demonstrated that the limiting...

A random vector (X1, ..., Xn), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x1 + ... + xn)x1a1.1 ... xnan.1 with theai all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a...

Let S = (1/n) [Sigma]t=1n X(t) X(t)', where X(1), ..., X(n) are p - 1 random vectors with mean zero. When X(t) (t = 1, ..., n) are independently and identically distributed (i.i.d.) as multivariate normal with mean vector 0 and covariance matrix [Sigma], many authors have investigated the...