The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

Aerodynamic roughness variation with vegetation: analysis in a suburban neighbourhood and a city park

Urban Ecosystems - Local aerodynamic roughness parameters (zero-plane displacement, z d , and aerodynamic roughness length, z 0 ) are determined for an urban park and a suburban neighbourhood with...     

Context Matters: Differential Effects of Discrimination by Environmental Context on Depressive Symptoms Among College Students of Color

Clinical Social Work Journal - Experiences with more subtle racism – which have been called microaggressions – have a host of negative effects on health, mental health, educational...     

Economic Stress, Quality of Life, and Mortality for the Oldest-Old in China

China??s oldest old population is estimated to quadruple by 2050. Yet, poverty rate for the oldest old has been the highest among all age groups in China. This paper investigates the relationship between economic stress, quality of life, and mortality among the oldest-old in China. Both objective economic hardships and perceived economic strain are examined. We base our investigation on data drawn from the Chinese Longitudinal Healthy Longevity Survey conducted between 2000 and 2005. Our sample includes 10,972 men and women between the ages of 80 and 105 in 2000. The data show that about 16% of these oldest-old lived under economic stress in 2000. The risk factors that make one vulnerable to economic stress include age, being male, being widowed or never married, being a minority member, having no education, having no living children, and not having children as main source of income, and having no pension. Economic stress is negatively associated with indicators of quality of life, such as the quality of medical care and mental well-being. The poor quality of life contributes to the higher mortality rate for the oldest old who are under economic stress. Results also show that perceived economic strain increases the risk of mortality by 42% in rural areas, even after controlling for basic demographic characteristics, life style factors, and major health events.?For the rural oldest-old, having children as a main source of income and having access to pension alleviates the negative impact of economic hardship on mortality hazard by 23 and 66% respectively. However, in urban areas, economic stress has no direct impact on the hazard of mortality.     

Reconfiguring Sovereignty in Foucauldian Genealogies of Power: The Case of English Master and Servant Law and the Dispersion and the Exercise of Sovereignty in the Modern Age

This paper is a critique and partial reconfiguration of the Foucauldian genealogy of sovereignty. Sovereignty is largely conceptualized as the antithesis of governmentality and disciplinary power in the modern age; presented as a negative case as a juridical and centralized power of interdiction and containment in the classical age. I argue that we can genealogically examine how sovereignty in the modern age underwent transformation and dispersion. My empirical focus is on how master and servant law in the eighteenth and nineteenth centuries, along with the development and transformations of local courts, led to the increasingly dispersal of sovereign power as it as practiced in specific industrial sites and regions.     

Information Seeking about Global Climate Change among Adolescents: The Role of Risk Perceptions, Efficacy Beliefs and Parental Influences

Global climate change is likely to have significant impacts on public health. Effective communication is critical to informing public decision making and behavior to mitigate climate change. An effective method of audience segmentation, the risk perception attitude (RPA) framework has been previously tested with other health behaviors and classifies people into 4 groups on the basis of their perceptions of risk and beliefs about personal efficacy. The 4 groups - indifference (low risk, weak efficacy), proactive (low risk, strong efficacy), avoidance (high risk, weak efficacy), and responsive (high risk, strong efficacy) - are hypothesized to differ in their self-protective behaviors and in their motivations to seek information. In this paper, we extend the RPA framework in two ways. First, we use it at the household level to determine whether parental classifications into the 4 groups are associated with their teenage children's classification into the same 4 groups. Second, we predict adolescent information-seeking behaviors on the basis of their and their parents' membership in the 4 RPA groups. Results (N = 523 parent-adolescent pairs) indicated that parental membership in the 4 RPA groups was significantly associated with children's membership in the same 4 groups. Furthermore, the RPA framework was a significant predictor of adolescent information-seeking: those in the responsive and avoidance groups sought more information on climate change than the indifference group. Family communication on global warming was positively associated with adolescents' information-seeking. Implications for interventions are discussed.     

Estimation for a first-order bifurcating autoregressive process with heavy-tail innovations

Asymptotics of an alternative extreme-value estimator for the autocorrelation parameter in a first-order bifurcating autoregressive (BAR) process with non-gaussian innovations are derived. This contrasts with traditional estimators whose asymptotic behavior depends on the central part of the innovation distribution. Within any BAR model, the main concern is addressing the complex dependency between generations. The inability of traditional methods to handle this dependency motivated an alternative procedure. With the combination of an extreme-value approach and a clever blocking argument, the dependency issue within the BAR process was resolved, which in turn allowed us to derive the limiting distribution for the proposed estimator through the use of regular variation and non-stationary point processes. Finally, the implications of our extreme-value approach are discussed with an extensive simulation study that not only assesses the reliability of our proposed estimate but also presents the findings for a new estimator of an unknown location parameter θ and its implications.     

Unconditional analogues of Cochran–Mantel–Haenszel tests

The Cochran–Mantel–Haenszel tests are a suite of tests that are usually defined as conditional tests, tests that assume all marginal totals are known before sighting the data. Here unconditional analogues of these tests are defined for the more usual situation when the marginal totals are not known before sighting the data.     

A general class of test statistics for Van Valen's Red Queen hypothesis

Van Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon age and the rate of extinction. We propose a general class of test statistics that can be used to test for the effect of age on the rate of extinction. These test statistics allow for a varying background rate of extinction and attempt to remove the effects of other covariates when assessing the effect of age on extinction. No model is assumed for the covariate effects. Instead we control for covariate effects by pairing or grouping together similar species. Simulations are used to compare the power of the statistics. We apply the test statistics to data on Foram extinctions and find that age has a positive effect on the rate of extinction. A derivation of the null distribution of one of the test statistics is provided in the supplementary material.     

Generating synthetic data to produce public-use microdata for small geographic areas based on complex sample survey data with application to the National Health Interview Survey

Small area statistics obtained from sample survey data provide a critical source of information used to study health, economic, and sociological trends. However, most large-scale sample surveys are not designed for the purpose of producing small area statistics. Moreover, data disseminators are prevented from releasing public-use microdata for small geographic areas for disclosure reasons; thus, limiting the utility of the data they collect. This research evaluates a synthetic data method, intended for data disseminators, for releasing public-use microdata for small geographic areas based on complex sample survey data. The method replaces all observed survey values with synthetic (or imputed) values generated from a hierarchical Bayesian model that explicitly accounts for complex sample design features, including stratification, clustering, and sampling weights. The method is applied to restricted microdata from the National Health Interview Survey and synthetic data are generated for both sampled and non-sampled small areas. The analytic validity of the resulting small area inferences is assessed by direct comparison with the actual data, a simulation study, and a cross-validation study.