A note on influence diagnostics in AR(1) time series models

The purpose of this paper is to develop influence diagnostics for AR(1) models under the innovative and the data perturbation schemes. There are four main contributions. First, we derive analytical expressions for the slope and curvature statistics. Second, we establish a relationship between the slope and curvature showing that the standardised slope and standardised curvature are equal for the innovative perturbation scheme, and these vectors are nearly identical for several values of the autoregressive parameter, for the data perturbation scheme. Third, we present a connection between the influence statistics and the tests for outlier detection. Fourth, for the innovative perturbation scheme, we derive the asymptotic distribution of a new influence statistic, whereas for the data perturbation scheme, the distribution of the influence statistics is obtained via Monte Carlo simulation. We additionally discuss practical guidelines for the use of local influence statistics, which are illustrated on a chemical process data set.     

On testing for independence between the innovations of several time series

Test statistics for checking the independence between the innovations of several time series are developed. The time series models considered allow for general specifications for the conditional mean and variance functions that could depend on common explanatory variables. In testing for independence between more than two time series, checking pairwise independence does not lead to consistent procedures. Thus a finite family of empirical processes relying on multivariate lagged residuals are constructed, and we derive their asymptotic distributions. In order to obtain simple asymptotic covariance structures, Möbius transformations of the empirical processes are studied, and simplifications occur. Under the null hypothesis of independence, we show that these transformed processes are asymptotically Gaussian, independent, and with tractable covariance functions not depending on the estimated parameters. Various procedures are discussed, including Cramér–von Mises test statistics and tests based on non‐parametric measures. The ranks of the residuals are considered in the new methods, giving test statistics which are asymptotically margin‐free. Generalized cross‐correlations are introduced, extending the concept of cross‐correlation to an arbitrary number of time series; portmanteau procedures based on them are discussed. In order to detect the dependence visually, graphical devices are proposed. Simulations are conducted to explore the finite sample properties of the methodology, which is found to be powerful against various types of alternatives when the independence is tested between two and three time series. An application is considered, using the daily log‐returns of Apple, Intel and Hewlett‐Packard traded on the Nasdaq financial market. The Canadian Journal of Statistics 40: 447–479; 2012 © 2012 Statistical Society of Canada     

It Takes Two to Tango: Couples’ Happiness and Childbearing

The existing literature has so far considered the role of the individual’s subjective well-being on fertility, neglecting the importance of the partner’s well-being. Using data from the British Household Panel Survey (BHPS) and event history models estimated separately by parity, we find that in a couple, women’s happiness matters more than that of the male partner in terms of having the first child. Specifically, we observe that couples in which either partner is happier than usual are more at risk of having the first child, but the effect is stronger with higher happiness of the woman. For the transition to the second child, we find that couples in which the woman declares to be happier or less happy than usual have a lower risk of childbirth. We, moreover, find support for a multiplicative effect of partners’ SWB on the decision to have a first child. Our results show that failing to acknowledge that the subjective well-being of both partners matters for the inherently joint decision making of childbearing can lead to an incomplete view of how subjective well-being affects fertility.     

Joint projections of temperature and precipitation change from multiple climate models: a hierarchical Bayesian approach

Summary.  Posterior distributions for the joint projections of future temperature and precipitation trends and changes are derived by applying a Bayesian hierachical model to a rich data set of simulated climate from general circulation models. The simulations that are analysed here constitute the future projections on which the Intergovernmental Panel on Climate Change based its recent summary report on the future of our planet's climate, albeit without any sophisticated statistical handling of the data. Here we quantify the uncertainty that is represented by the variable results of the various models and their limited ability to represent the observed climate both at global and at regional scales. We do so in a Bayesian framework, by estimating posterior distributions of the climate change signals in terms of trends or differences between future and current periods, and we fully characterize the uncertain nature of a suite of other parameters, like biases, correlation terms and model-specific precisions. Besides presenting our results in terms of posterior distributions of the climate signals, we offer as an alternative representation of the uncertainties in climate change projections the use of the posterior predictive distribution of a new model's projections. The results from our analysis can find straightforward applications in impact studies, which necessitate not only best guesses but also a full representation of the uncertainty in climate change projections. For water resource and crop models, for example, it is vital to use joint projections of temperature and precipitation to represent the characteristics of future climate best, and our statistical analysis delivers just that.     

Remember the curse of dimensionality: the case of goodness-of-fit testing in arbitrary dimension

Despite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions, there is no mention there of any curse of dimensionality. In fact, in some publications, a parametric rate is derived. As we discuss below, this is because a directional alternative is considered. Indeed, even in dimension one, Ingster, Y. I. [(1987). Minimax testing of nonparametric hypotheses on a distribution density in the l_p metrics. Theory of Probability & Its Applications, 31(2), 333–337] has shown that the minimax rate is not parametric. In this paper, we extend his results to arbitrary dimension and confirm that the minimax rate is not only nonparametric, exhibits but also a prototypical curse of dimensionality. We further extend Ingster's work to show that the chi-squared test achieves the minimax rate. Moreover, we show that the test adapts to the intrinsic dimensionality of the data. Finally, in the spirit of Ingster, Y. I. [(2000). Adaptive chi-square tests. Journal of Mathematical Sciences, 99(2), 1110–1119], we consider a multiscale version of the chi-square test, showing that one can adapt to unknown smoothness without much loss in power.     

Investigation of mixed model repeated measures analyses and non‐linear random coefficient models in the context of long‐term efficacy data

The longitudinal data from 2 published clinical trials in adult subjects with upper limb spasticity (a randomized placebo‐controlled study [NCT01313299] and its long‐term open‐label extension [NCT01313312]) were combined. Their study designs involved repeat intramuscular injections of abobotulinumtoxinA (Dysport®), and efficacy endpoints were collected accordingly. With the objective of characterizing the pattern of response across cycles, Mixed Model Repeated Measures analyses and Non‐Linear Random Coefficient (NLRC) analyses were performed and their results compared. The Mixed Model Repeated Measures analyses, commonly used in the context of repeated measures with missing dependent data, did not involve any parametric shape for the curve of changes over time. Based on clinical expectations, the NLRC included a negative exponential function of the number of treatment cycles, with its asymptote and rate included as random coefficients in the model. Our analysis focused on 2 specific efficacy parameters reflecting complementary aspects of efficacy in the study population. A simulation study based on a similar study design was also performed to further assess the performance of each method under different patterns of response over time. This highlighted a gain of precision with the NLRC model, and most importantly the need for its assumptions to be verified to avoid potentially biased estimates. These analyses describe a typical situation and the conditions under which non‐linear mixed modeling can provide additional insights on the behavior of efficacy parameters over time. Indeed, the resulting estimates from the negative exponential NLRC can help determine the expected maximal effect and the treatment duration required to reach it.     

整个世界都在变成科学元勘——法迪勒·马赞德兰尼对话布鲁诺·拉图尔

如何在这片森林中生存?如何使之保持活力?拉图尔就当前的全球生态危机提出了这些问题,但当应用于STS的森林——或者用拉图尔自己的隐喻生物多样性时,这些问题也同样恰当.在访谈中,拉图尔描绘了一幅STS生存模式的特殊图景.在这一图景中,STS既非对科学的批判也非对科学的辅助,而是通过教育与合作将不言而喻的STS敏感性融入科学之中.尽管拉图尔承认STS领域在立场和进路上存在诸多差异,但他淡化了这些差异,将所有感染STS人的定义特征设定为共同致力于将以大写的S开头的科学(Science)转化为一些可以进行经验研究的问题.毫无疑问,他所描绘的是一幅建构主义的图景,社会科学家和自然科学家、工程师、艺术家以及政治家们在其中共同建设世界.     

Determinants of Health and the Quality of Life in the Bella Coola Valley

The aim of this investigation is to obtain some baseline self-reported data on the health status and overall quality of life of all residents of the Bella Coola Valley of British Columbia aged 17 years or older, and to measure the impact of a set of designated health determinants on their health and quality of life. In the period from August to November 2001, a variety of procedures were used to ensure that all eligible residents of the Valley received a copy of our questionnaire, and 687 useable questionnaires were obtained for our working dataset. Health status was measured by SF-36 and the U.S. Centers for Disease Control healthy days items. Thirty-one items were used to measure the Provincial Health Officer’s designated determinants of health in four clusters, namely, biological, social and economic, health behaviours and health services determinants. Quality of life was measured by satisfaction levels in 13 specific domains of life (e.g., family, financial security), four global items (e.g., happiness, life satisfaction) and one global Subjective Well-Being Index. Besides obtaining baseline figures on all our measures for the Valley, we made some comparisons among our figures and those from other areas, e.g., Prince George, BC. Most of the measures indicated that the health status and quality of life of Bella Coola Valley residents were lower than those of Prince George residents. For the sample as a whole, SF-36 scores on the eight dimensions ran from 82.3 (physical functioning) to 50.0 (social functioning), with a mean of 62.7. Residents in the Valley averaged 6.5 days in the past 30 in which their health was physically not good, 5.5 days when it was mentally not good and 4.1 days when their health limited their usual daily activities. Eleven percent of respondents described their general health as “excellent” and another 27% said it was “very good”. On a 7-point scale from 1=very dissatisfied to 7=very satisfied, respondents had average life satisfaction and satisfaction with the overall quality of life scores of 5.5. For specific domains of life, the lowest mean level of satisfaction was reported for federal and provincial government officials (3.3) and the highest was reported for living partners and personal safety around home (5.8). Regarding bivariate relations, each of the eight dimensions of SF-36 was significantly correlated with a single item measure of general health, and five of the eight were significantly correlated with the number of good health days. Happiness and the Subjective Well-Being Index were positively but moderately correlated with six of the eight dimensions, and life satisfaction was positively correlated with five. Age was negatively related to general health, but positively related to life satisfaction. Not being of aboriginal descent was positively related to all of the four global health indicators and to the Subjective Well-Being Index. Education was positively related to the four global health measures but not to the three global quality of life measures. The Social Support and Good Family Indexes were positively related to all seven global measures. There was a positive correlation between six of the seven global measures and the frequency with which respondents participated in activities sponsored by voluntary organizations. Frequency of smoking was negatively associated with every global dependent variable except the Physical Health Index. Frequency of skipping meals was negatively associated and average hours of sleep per night was positively associated with all seven global measures. Turning to multivariate relationships, the four clusters of health determinants explained from 12% (SF-36 Mental Health Index) to 24% (general health) of the variance in the dependent global health variables, and from 20% (happiness) to 26% (Subjective Well-Being Index) of the variance in the dependent global quality of life variables. Adding domain satisfaction scores to the total set of predictors allowed us to explain from 20% (SF-36 Mental health Index) to 29% (general health) of the variance in the dependent global health variables, and from 39% (happiness) to 62% (life satisfaction) in the dependent global quality of life variables. By including measures of social support and good family relationships in our set of health determinants, we practically guaranteed that the latter would be relatively strongly predictive of global quality of life.     

Bayesian deconvolution of oil well test data using Gaussian processes

We use Bayesian methods to infer an unobserved function that is convolved with a known kernel. Our method is based on the assumption that the function of interest is a Gaussian process and, assuming a particular correlation structure, the resulting convolution is also a Gaussian process. This fact is used to obtain inferences regarding the unobserved process, effectively providing a deconvolution method. We apply the methodology to the problem of estimating the parameters of an oil reservoir from well-test pressure data. Here, the unknown process describes the structure of the well. Applications to data from Mexican oil wells show very accurate results.     

New Results for Computing Blaker’s Exact Confidence Interval for One Parameter Discrete Distributions

The authors state new general results for computing Blaker’s exact confidence interval limits for usual one-parameter discrete distributions. Specific results for implementing an accurate and fast algorithm are made explicit for the binomial, negative binomial, Poisson and hypergeometric model.