The exact noncentral distribution of the generalized multiple correlation matrix

Given p×n X N(βY, ∑?I), β, ∑ unknown, the noncentral multivariate beta density of the matrix L = [(YY′)^-1/2Y X′ (XX′)^-1XY′ (YY′)^-1/2] is desired. Khatri (1964) finds this density when β is of rank unity. The present paper derives the noncentral density of L and the density of the roots matrix of L for full rank β. The dual case density of L is also obtained. The derivations are based on generalized Sverdrup's lemma, Kabe (1965), and the relationship between primal and dual density of L is explicitly established.     

MSE-matrix superiority of the mixed over the least squares estimator in the presence of outliers

In his recent paper, Ali (1991) has shown that the mixed regression estimator, when data contain mean-shift or variance inflation outliers, is uniformly superior to the ordinary least squares estimator in terms of scalar-valued mean square error. However, when using the matrix-valued mean square error criterion, this dominance fails to hold in general. The subsequent investigation gives a complete characterization of the situation where the mixed estimator is superior to the LS-estimator when the comparison is made with respect to this stronger MSE-property. Vice versa, the LS-estimator never dominates the mixed estimator relative to this criterion.     

A note on second order slope rotatable designs over all directions

Hader and Park (1978) introduced second order slope rotatability in axial directions. Park (1987) introduced second order slope rotatabilty over all directions. It is shown that these designs have the additional properly that the sum of the variances of estimates of slopes in all directions at any point is a function of the distance of the point from the design origin.     

Risk analysis of PCB exposure via the soil-food crop pathway, and alternatives for remediation at Serpukhov, Russian Federation.

A risk assessment was conducted to determine the likelihood of certain health risks resulting from exposure to soils and food crops contaminated with polychlorinated biphenyl (PCBs). PCBs have contaminated soils, river sediments, and air in the past as a result of industrial activities at a capacitor plant located in the City of Serpukhov, Russian Federation. This risk assessment and suggestions for remediation are designed to aid in decision-making efforts by a joint Russian-American research team developing a community, national, and international response to industrial contamination. Bobovnikova et al. (The Science of the Total Environment 139/140, 357-364, [1993]) have reported that PCBs are elevated in soils and sediments, breast milk, and locally grown foods in the Serpukhov area. Data from these and other investigators have been used in this risk assessment to calculate a potential cancer risk resulting from exposure to PCBs. Our assessment indicates that members of the local population may be at increased risk of cancer, and possibly other adverse health effects, as a result of PCB contamination of their environment. Because previously unassessed environmental contamination is a common problem in the former Soviet Republics, as well as many other areas of the world, we believe this type of evaluation, using known methods, can serve as a model for assessment efforts in other parts of the globe and result in remediative efforts in regions constrained by faltering economies.     

Book review

New Zealand and the European Union edited by Matthew Gibbons. Auckland, Pearson Education. 2008. 172 p. NZ$52.99 (paperback). ISBN 0733993831.

Going bush. New Zealanders and nature in the twentieth century by Kirstie Ross. Auckland, Auckland University Press. 2008. 200 p. NZ$34.99 (paperback). ISBN 1869404246.

Globalisation and the wealth of nations by Brian Easton. Auckland, Auckland University Press. 2007. 248 p. NZ$50.00 (paperback). ISBN 9781869403775.     

Combined estimate of a location parameter

In this paper, we revisit the problem of combining estimates of location considered by Cohen (1976). Our results unify and strengthen the results of Cohen (1976), Bhattacharya (1981) and Akai (1982).     

Bling bling taxation and the fiscal virtues of hip hop

The article extends Ng’s (Am Econ Rev 77(1):186–191, 1987) model of optimal taxation of diamond goods—goods that are valued solely for their costliness. We extend his findings by analyzing how other goods should be taxed in the presence of pure diamond goods; modified Ramsey rules are derived in a basic single-type model as well as in a two-type model with redistribution. One key finding, that may be surprising and rather provoking, is that close complements (hip hop music) to diamond goods (bling bling) should be heavily subsidized.     

Non-linear models 1

This is the first application of a new method for testing stationary random point processes. Consider the class of all stationary ergodic point processes on the real line with arbitrary dependences among the inter–point distances (spacing).The hypothesis is :The observed process φ is a homogeneous Poisson process or more (resp.less) regular than a Poisson process.The sample is the vector of the first n points t₁, …,t_n.There is a close relation between our method for testing and queueing theory: For finding an appropriate test statistic, we observe the behaviour of a single server queue with the input φ.A table of critical values is given.     

Managing green productivity: Some strategic directions

The twentieth century has been the hallmark for managing total productivity, where the emphasis is towards maximization of outputs commensurate with the consumption of inputs. This is being challenged now to evolve the world class manufacturing strategy requiring a paradigm shift. This shift is towards green productivity, which looks forward to socially appropriate production and consumption aiming at value innovation and resource conservation. This paper is an attempt to outline the concepts and experiential learning about green productivity.     

A clustering approach to interpretable principal components

A new method for constructing interpretable principal components is proposed. The method first clusters the variables, and then interpretable (sparse) components are constructed from the correlation matrices of the clustered variables. For the first step of the method, a new weighted-variances method for clustering variables is proposed. It reflects the nature of the problem that the interpretable components should maximize the explained variance and thus provide sparse dimension reduction. An important feature of the new clustering procedure is that the optimal number of clusters (and components) can be determined in a non-subjective manner. The new method is illustrated using well-known simulated and real data sets. It clearly outperforms many existing methods for sparse principal component analysis in terms of both explained variance and sparseness.