Empirical bayes shrinkage estimation of reliability in the exponential distribution

In this paper we propose two empirical Bayes shrinkage estimators for the reliability of the exponential distribution and study their properties. Under the uniform prior distribution and the inverted gamma prior distribution these estimators are developed and compared with a preliminary test estimator and with a shrinkage testimator in terms of mean squared error. The proposed empirical Bayes shrinkage estimator under the inverted gamma prior distribution is shown to be preferable to the preliminary test estimator and the shrinkage testimator when the prior value of mean life is clsoe to the true mean life.     

Modelling udder infection data using copula models for quadruples

We study copula models for correlated infection times in the four udder quarters of dairy cows. Both a semi-parametric and a nonparametric approach are considered to estimate the marginal survival functions, taking into account the effect of a binary udder quarter level covariate. We use a two-stage estimation approach and we briefly discuss the asymptotic behaviour of the estimators obtained in the first and the second stage of the estimation. A pseudo-likelihood ratio test is used to select an appropriate copula from the power variance copula family that describes the association between the outcomes in a cluster. We propose a new bootstrap algorithm to obtain the p-value for this test. This bootstrap algorithm also provides estimates for the standard errors of the estimated parameters in the copula. The proposed methods are applied to the udder infection data. A small simulation study for a setting similar to the setting of the udder infection data gives evidence that the proposed method provides a valid approach to select an appropriate copula within the power variance copula family.     

Amplification of Sensitivity Analysis in Matched Observational Studies

A sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed. In matched observational studies of treatment effects, a key assumption in some analyses is that subjects matched for observed covariates are comparable, and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching. What properties would such an unobserved covariate need to have to materially alter the inference about treatment effects? For ease of calculation and reporting, it is convenient that the sensitivity analysis be of low dimension, perhaps indexed by a scalar sensitivity parameter, but for interpretation in specific contexts, a higher dimensional analysis may be of greater relevance. An amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points, perhaps a 'curve,' in a higher dimensional sensitivity analysis such that the possible inferences are the same for all points in the set. Possessing an amplification, an investigator may calculate and report the low dimensional analysis, yet have available the interpretations of the higher dimensional analysis.     

Estimation in capture–recapture models when covariates are subject to measurement errors and missing data

For capture–recapture models when covariates are subject to measurement errors and missing data, a set of estimating equations is constructed to estimate population size and relevant parameters. These estimating equations can be solved by an algorithm similar to the EM algorithm. The proposed method is also applicable to the situation when covariates with no measurement errors have missing data. Simulation studies are used to assess the performance of the proposed estimator. The estimator is also applied to a capture–recapture experiment on the bird species Prinia flaviventris in Hong Kong. The Canadian Journal of Statistics 37: 645–658; 2009 © 2009 Statistical Society of Canada     

Profile upper Confidence Limits from Discrete Data

When the data are discrete, standard approximate confidence limits often have coverage well below nominal for some parameter values. While ad hoc adjustments may largely solve this problem for particular cases, Kabaila & Lloyd (1997) gave a more systematic method of adjustment which leads to tight upper limits, which have coverage which is never below nominal and are as small as possible within a particular class. However, their computation for all but the simplest models is infeasible. This paper suggests modifying tight upper limits by an initial replacement of the unknown nuisance parameter vector by its profile maximum likelihood estimator. While the resulting limits no longer possess the optimal properties of tight limits exactly, the paper presents both numerical and theoretical evidence that the resulting coverage function is close to optimal. Moreover these profile upper limits are much (possibly many orders of magnitude) easier to compute than tight upper limits.     

Attenuating Initial Beliefs: Increasing the Acceptance of Anthropogenic Climate Change Information by Reflecting on Values

Anthropogenic climate change information tends to be interpreted against the backdrop of initial environmental beliefs, which can lead to some people being resistant toward the information. In this article (N = 88), we examined whether self‐affirmation via reflection on personally important values could attenuate the impact of initial beliefs on the acceptance of anthropogenic climate change evidence. Our findings showed that initial beliefs about the human impact on ecological stability influenced the acceptance of information only among nonaffirmed participants. Self‐affirmed participants who were initially resistant toward the information showed stronger beliefs in the existence of climate change risks and greater acknowledgment that individual efficacy has a role to play in reducing climate change risks than did their nonaffirmed counterparts.     

A Tiered Framework for Risk‐Relevant Characterization and Ranking of Chemical Exposures: Applications to the National Children's Study (NCS)

A challenge for large‐scale environmental health investigations such as the National Children's Study (NCS), is characterizing exposures to multiple, co‐occurring chemical agents with varying spatiotemporal concentrations and consequences modulated by biochemical, physiological, behavioral, socioeconomic, and environmental factors. Such investigations can benefit from systematic retrieval, analysis, and integration of diverse extant information on both contaminant patterns and exposure‐relevant factors. This requires development, evaluation, and deployment of informatics methods that support flexible access and analysis of multiattribute data across multiple spatiotemporal scales. A new “Tiered Exposure Ranking” (TiER) framework, developed to support various aspects of risk‐relevant exposure characterization, is described here, with examples demonstrating its application to the NCS. TiER utilizes advances in informatics computational methods, extant database content and availability, and integrative environmental/exposure/biological modeling to support both “discovery‐driven” and “hypothesis‐driven” analyses. “Tier 1” applications focus on “exposomic” pattern recognition for extracting information from multidimensional data sets, whereas second and higher tier applications utilize mechanistic models to develop risk‐relevant exposure metrics for populations and individuals. In this article, “tier 1” applications of TiER explore identification of potentially causative associations among risk factors, for prioritizing further studies, by considering publicly available demographic/socioeconomic, behavioral, and environmental data in relation to two health endpoints (preterm birth and low birth weight). A “tier 2” application develops estimates of pollutant mixture inhalation exposure indices for NCS counties, formulated to support risk characterization for these endpoints. Applications of TiER demonstrate the feasibility of developing risk‐relevant exposure characterizations for pollutants using extant environmental and demographic/socioeconomic data.