This multi-author report is the product of collaborative interdisciplinary research about the use of the precautionary and adaptive management principles in administrative decision-making when faced with scientific uncertainty. Using four case studies about genetically modified organisms, pesticides, fisheries and invasive species, the report discusses (i) how the principles of precaution and adaptive management are understood and applied; (ii) how their introduction might affect the operation of traditional administrative law values (fairness, legitimacy and effectiveness); and, (iii) how the new principles may be most appropriately accommodated within the general framework of administrative law values. The authors observe that the precaution, adaptive management and administrative law principles must be framed and applied in a way that reflects the social values that support their existence, and will thus be influenced by the context in which administrative decisions are made. The report concludes with recommendations for standards of review in administrative law, accounting for various factors: expertise, participation, evidentiary and other procedural rules and mechanisms for review and accountability.

Consider a multiclass M / G /1 queue where queued customers are served in their order of arrival at a rate which depends on the customer class. We model this system using a chain with states represented by a tree. Since the service time distribution depends on the customer class, the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Nevertheless, we can find a harmonic function on this chain which provides information about the asymptotics of this stationary distribution. The associated h ‐transformation produces a change of measure that increases the arrival rate of customers and decreases the departure rate thus making large deviations common. The Canadian Journal of Statistics 37: 327–346; 2009 © 2009 Statistical Society of Canada

The authors define the scaled empirical point process. They obtain the weak limit of these point processes through a novel use of a dimension‐free method based on the convergence of compensators of multiparameter martingales. The method extends previous results in several directions. They obtain limits at points where the density may be zero, but has regular variation. The joint limit of the empirical process evaluated at distinct points is given by independent Poisson processes. They provide applications both to nearest‐neighbour density estimation in high dimensions, and to the asymptotic behaviour of multivariate extremes such as those arising from bivariate normal copulas. The Canadian Journal of Statistics 37: 347–360; 2009 © 2009 Statistical Society of Canada

Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point processes through a novel use of a dimension-free method based on the convergence of compensators of multiparameter martingales. The method extends previous results in several directions. We obtain limits at points where the density of $Y_i$ may be zero, but has regular variation. The joint limit of the empirical process evaluated at distinct points is given by independent Poisson processes. These results also hold for multivariate $Y_i$ with little additional effort. Applications are provided both to nearest-neighbour density estimation in high dimensions, and to the asymptotic behaviour of multivariate extremes such as those arising from bivariate normal copulas.

In this paper we study the conditional distribution of a multinomial sample, given certain marginals. By direct evaluation of the probabilities using Stirling's formula we obtain a local limit theorem. The limit distribution turns out to be multivariate normal and we can identify the covariance matrix. Consequently we prove asymptotic normality of the H-coefficient in certain nonparametric unfolding models with dichotomous data.

Consider a random integer-valued process X(t) on Z(+) that satisfies some weak dependence condition. We study the empirical distribution function of the occupation times of such a process and prove convergence to a suitable Gaussian process. An application to the statistical analysis of open and closed sojourn-time distributions for ion channels is provided.

The positive dependence notion of association for collections of random variables is generalized to that of weak association for collections of vector valued random elements in such a way as to allow negative dependencies in individual random elements. An invariance principle is stated and proven for a stationary, weakly associated sequence of Rd-valued or separable Hilbert space valued random elements which satisfy a covariance summability condition.

We give a simpler proof of the probability invariance principle for triangular arrays of independent identically distributed random variables with values in a separable Banach space, recently proved by de Acosta [1], and improve this result to an almost sure invariance principle.