High-breakdown linear discriminant analysis

The classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come. Because these true parameters are generally unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. However, these sample statistics are notoriously susceptible to contamination by outliers, a problem compounded by the fact that the outliers may be invisible to conventional diagnostics. High-breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers, regardless of their severity. In this article we motivate and develop a high-breakdown criterion for linear discriminant analysis and give an algorithm for its implementation. The procedure is intended to supplement rather than replace the usual sample-moment methodology of discriminant analysis either by providing indications that the dataset is not seriously affected by outliers (supporting the usual analysis) or by identifying apparently aberrant points and giving resistant estimators that are not affected by them.

Dietary trends: Estimates from food supply and survey data

Objective: To illustrate methodological issues involved in estimating dietary trends in populations using data obtained from various sources in Australia in the 1980s and 1990s. Methods: Estimates of absolute and relative change in consumption of selected food items were calculated using national data published annually on the national food supply for 1982-83 to 1992-93 and responses to food frequency questions in two population based risk factor surveys in 1983 and 1994 in the Hunter Region of New South Wales, Australia. The validity of estimated food quantities obtained from these inexpensive sources at the beginning of the period was assessed by comparison with data from a national dietary survey conducted in 1983 using 24 h recall. Results: Trend estimates from the food supply data and risk factor survey data were in good agreement for increases in consumption of fresh fruit, vegetables and breakfast food and decreases in butter, margarine, sugar and alcohol. Estimates for trends in milk, eggs and bread consumption, however, were inconsistent. Conclusions: Both data sources can be used for monitoring progress towards national nutrition goals based on selected food items provided that some limitations are recognized. While data collection methods should be consistent over time they also need to allow for changes in the food supply (for example the introduction of new varieties such as low-fat dairy products). From time to time the trends derived from these inexpensive data sources should be compared with data derived from more detailed and quantitative estimates of dietary intake.

Finite element analysis of mechanical properties in discontinuously reinforced metal matrix composites with ultrafine microstructure

This investigation focused on the finite element analyses of elastic and plastic properties of aluminium/alumina composite materials with ultrafine microstructure. The commonly used unit cell model was used to predict the elastic properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the plastic properties of the composites and the associated strengthening mechanism within the metal matrix material were investigated. The grain size of the matrix material was found to be an important factor influencing the mechanical properties of the composites studied. (C) 1997 Elsevier Science S.A.

Estimating correlations from epidemiological data in the presence of measurement error

Analysis of a major multi-site epidemiologic study of heart disease has required estimation of the pairwise correlation of several measurements across sub-populations. Because the measurements from each sub-population were subject to sampling variability, the Pearson product moment estimator of these correlations produces biased estimates. This paper proposes a model that takes into account within and between sub-population variation, provides algorithms for obtaining maximum likelihood estimates of these correlations and discusses several approaches for obtaining interval estimates. (C) 1997 by John Wiley & Sons, Ltd.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.