Reflections on liberalism,policulturalism, and ID-ology: citizenship and difference in South Africa

How do nation-states in the twenty-first century, nation-states increasingly forced to come to terms with the ethnic heterogeneity of their citizens, deal with the problem of cultural difference? How, in particular, does the Constitution of post-apartheid South Africa — widely believed to be the most enlightened in the contemporary world, the most tolerant of diversity — strike a balance between the ‘One Law’ of ‘The Nation’ and the plurality of customary beliefs sustained, as a matter of right, by the various peoples who make up this postcolony? What happens, in the course of everyday existence, when Constitution and Custom appear to contradict one another — and to do so in such a manner as to raise questions of basic human rights, of freedom of belief, even of life-and-death? These questions are addressed in the paper through a critical, broadly situated analysis of the confrontation between the Constitution of South Africa and the Kingdom of Custom that continues to prevail in one of its provinces, the North West. By exploring a complicated case that drew the State, via its Human Rights Commission, into open conflict with a Tswana chiefdom — a case about death rituals argued, before a high court judge, in the lexicon of modern jurisprudence — it shows how a ‘living constitution’, tolerant of everyday ambiguity, is being forged in the space of strategic engagement opened up by the alternative languages and cultures of legality that exist in this ‘policultural’ postcolony. And in others like it.     

Multivariate Kendall's tau for change‐point detection in copulas

Statistical procedures for the detection of a change in the dependence structure of a series of multivariate observations are studied in this work. The test statistics that are proposed are $L_1$ , $L_2$ , and $L_{\infty }$ distances computed from vectors of differences of Kendall's tau; two multivariate extensions of Kendall's measure of association are used. Since the distributions of these statistics under the null hypothesis of no change depend on the unknown underlying copula of the vectors, a procedure based on the multiplier central limit theorem is used for the computation of p‐values; the method is shown to be valid both asymptotically and for moderate sample sizes. Alternative versions of the tests that take into account possible breakpoints in the marginal distributions are also investigated. Monte Carlo simulations show that the tests are powerful under many scenarios of change‐point. In addition, two estimators of the time of change are proposed and their efficiency is carefully studied. The methodologies are illustrated on simulated series from the Canadian Regional Climate Model. The Canadian Journal of Statistics 41: 65–82; 2013 © 2012 Statistical Society of Canada     

A comparison of test statistics for the recovery of rapid growth‐based enumeration tests

This paper considers five test statistics for comparing the recovery of a rapid growth‐based enumeration test with respect to the compendial microbiological method using a specific nonserial dilution experiment. The finite sample distributions of these test statistics are unknown, because they are functions of correlated count data. A simulation study is conducted to investigate the type I and type II error rates. For a balanced experimental design, the likelihood ratio test and the main effects analysis of variance (ANOVA) test for microbiological methods demonstrated nominal values for the type I error rate and provided the highest power compared with a test on weighted averages and two other ANOVA tests. The likelihood ratio test is preferred because it can also be used for unbalanced designs. It is demonstrated that an increase in power can only be achieved by an increase in the spiked number of organisms used in the experiment. The power is surprisingly not affected by the number of dilutions or the number of test samples. A real case study is provided to illustrate the theory. Copyright © 2013 John Wiley & Sons, Ltd.     

Maximum Likelihood Estimation for Stochastic Differential Equations with Random Effects

Abstract. We consider N independent stochastic processes (X _i (t), t ∈ [0,T _i ]), i=1,…, N, defined by a stochastic differential equation with drift term depending on a random variable φ _i . The distribution of the random effect φ _i depends on unknown parameters which are to be estimated from the continuous observation of the processes X_i. We give the expression of the exact likelihood. When the drift term depends linearly on the random effect φ _i and φ _i has Gaussian distribution, an explicit formula for the likelihood is obtained. We prove that the maximum likelihood estimator is consistent and asymptotically Gaussian, when T _i =T for all i and N tends to infinity. We discuss the case of discrete observations. Estimators are computed on simulated data for several models and show good performances even when the length time interval of observations is not very large.     

A Question of Ethics

This article identifies three consulting roles—helper, leader, and colleague; recommends that statistical consultants ask more questions about basic mechanisms; suggests that statistical consultants regard their primary responsibility as providing guidance about the scientific method itself; discusses the need for continuing education to help improve consulting skills; and describes Wisconsin's Master's degree examination, which was designed to help students become effective practicing statisticians.     

Parameter measures of skewness

Several different measures of skewness are commonly used in place of γ₁, the third central moment divided by the cube of the standard deviation. The numerical values of these measures are compared in this paper for members of the gamma, lognormal or Weibull family of distributions and shown to vary considerably in most cases even when skewness and kurtosis are moderate.