This paper informs a statistical readership about Artificial Neural Networks (ANNs), points out some of the links with statistical methodology and encourages cross-disciplinary research in the directions most likely to bear fruit. The areas of statistical interest are briefly outlined, and a series of examples indicates the flavor of ANN models. We then treat various topics in more depth. In each case, we describe the neural network architectures and training rules and provide a statistical commentary. The topics treated in this way are perceptrons (from single-unit to multilayer versions), Hopfield-type recurrent networks (including probabilistic versions strongly related to statistical physics and Gibbs distributions) and associative memory networks trained by so-called unsuperviszd learning rules. Perceptrons are shown to have strong associations with discriminant analysis and regression, and unsupervized networks with cluster analysis. The paper concludes with some thoughts on the future of the interface between neural networks and statistics.

Small area estimation is becoming important in survey sampling due to a growing demand for reliable small area statistics from both public and private sectors. It is now widely recognized that direct survey estimates for small areas are likely to yield unacceptably large standard errors due to the smallness of sample sizes in the areas. This makes it necessary to "borrow strength" from related areas to find more accurate estimates for a given area or, simultaneously, for several areas. This has led to the development of alternative methods such as synthetic, sample size dependent, empirical best linear unbiased prediction, empirical Bayes and hierarchical Bayes estimation. The present article is largely an appraisal of some of these methods. The performance of these methods is also evaluated using some synthetic data resembling a business population. Empirical best linear unbiased prediction as well as empirical and hierarchical Bayes, for most purposes, seem to have a distinct advantage over other methods.

This is a study of the use of citation data to investigate the role statistics journals play in communication within that field and between statistics and other fields. The study looks at citations as import-export statistics reflecting intellectual influence. The principal findings include: there is little variability in both the number and diversity of imports, but great variability in both the number and diversity of exports and hence in the balance of trade; there is a tendency for influence to flow from theory to applications to a much greater extent than in the reverse direction; there is little communication between statistics and probability journals. The export scores model is introduced and employed to map a set of journals' bilateral intellectual influences onto a one-dimensional scale, and the Cox effect is identified as a phenomenon that can occur when a disciplinary paper attracts a large degree of attention from outside its discipline.

In this paper, we demonstrate some properties of $\alpha$-stable (stable) random variables and processes. It turns out that with the use of suitable statistical estimation techniques, computer simulation procedures and numerical discretization methods it is possible to construct approximations of stochastic integrals with stable measures as integrators. As a consequence we obtain an effective, general method giving approximate solutions for a wide class of stochastic differential equations involving such integrals. Application of computer graphics provides interesting quantitative and visual information on those features of stable variates which distinguish them from their commonly used Gaussian counterparts. It is possible to demonstrate evolution in time of densities with heavy tails of appropriate processes, to visualize the effect of jumps of trajectories, etc. We try to demonstrate that stable variates can be very useful in stochastic modeling of problems of different kinds, arising in science and engineering, which often provide better description of real life phenomena than their Gaussian counterparts.