Unit roots and double smooth transitions

Techniques for testing the null hypothesis of difference stationarity against stationarity around some deterministic function have received much attention. In particular, unit root tests where the alternative is stationarity around a smooth transition in a linear trend have recently been proposed to permit the possibility of non-instantaneous structural change. In this paper we develop tests extending such an approach in order to admit more than one structural change. The analysis is motivated by time series that appear to undergo two smooth transitions in the linear trend, and the application of the new tests to two such series (average global temperature and US consumer prices) highlights the benefits of this double transition extension.     

Interval estimation via tail functions

The authors describe a new method for constructing confidence intervals. Their idea consists in specifying the cutoff points in terms of a function of the target parameter rather than as constants. When it is suitably chosen, this so‐called tail function yields shorter confidence intervals in the presence of prior information. It can also be used to improve the coverage properties of approximate confidence intervals. The authors illustrate their technique by application to interval estimation of the mean of Bernoulli and normal populations. They further suggest guidelines for choosing the optimal tail function and discuss the relationship with Bayesian inference.     

THE EPIDEMIOLOGY OF A DISEASE USING HAZARD FUNCTIONS1

A prime objective of this paper is to mathematically quantify certain epidemiological concepts and show how some of these can be applied to certain registry type data. Usually epidemiological quantities are expressed in terms of density functions. However it is often more natural to estimate hazard functions in practical situations. Hence the emphasis will be on expressing various measures in terms of hazard functions. This contrasts with the useful paper of Albert, Gertman & Louis (1978) where density functions are used throughout. The definitions of some key concepts such as cohort effect are also different which gives rise to an alternative analysis and some new results. Initially, incidence, mortality and prevalence are discussed and this is followed by a treatment of initiation which is a less commonly used measure. The results are applied to the lung cancer data in the South Australian Central Cancer Registry.     

Moving images: The media representation of refugees

The paper takes the form of a broad-based exploration of the visual representations of refugees across a range of media forms. Firstly it suggests that these media images have origins in Christian iconography. Then the discussion considers the treatment of forced migration in the fiction film, proposing that cinema representations often conform to the "road movie" genre. A discussion of contemporary issues in the media representation of refugees points to the necessity and direction for future research on the subject.     

Two Birthday Problems

ABSTRACT

This article focuses on two birthday problems which naturally follow from the most common birthday problems taught in statistics courses. The solutions to these new problems provide a good illustration of several combinatorial techniques.     

Estimating Moments of Subjectively Assessed Distributions*

Moment‐matching discrete distributions were developed by Miller and Rice (1983) as a method to translate continuous probability distributions into discrete distributions for use in decision and risk analysis. Using gaussian quadrature, they showed that an n‐point discrete distribution can be constructed that exactly matches the first 2n ‐ 1 moments of the underlying distribution. These moment‐matching discrete distributions offer several theoretical advantages over the typical discrete approximations as shown in Smith (1993), but they also pose practical problems. In particular, how does the analyst estimate the moments given only the subjective assessments of the continuous probability distribution? Smith suggests that the moments can be estimated by fitting a distribution to the assessments. This research note shows that the quality of the moment estimates cannot be judged solely by how close the fitted distribution is to the true distribution. Examples are used to show that the relative errors in higher order moment estimates can be greater than 100%, even though the cumulative distribution function is estimated within a Kolmogorov‐Smirnov distance less than 1%.     

Sensitivity Analysis for Dependent Variables*

Decision analysts use sensitivity analysis to identify influential variables, to determine which input variables to model stochastically, and to characterize scenarios that could affect a change in the rank ordering of the alternatives. A frequently recommended sensitivity analysis technique is “one‐way” sensitivity analysis, which determines a variable's influence by the degree to which the objective function changes as that variable is varied while all other variables are held fixed. Disadvantages of one‐way analysis are that it measures the influence of only one variable at a time and it assumes independence among the input variables. Clearly, however, there are situations when dependencies exist among the input variables that could possibly affect the sensitivity analysis results. This research develops a strategy that incorporates dependence relations among the input variables into the sensitivity analysis using rank correlations. Only decision problems with a finite number of alternatives and continuous state variables are considered.