TWO‐ AND THREE‐STAGE FLOWSHOP SCHEDULING WITH NO‐WAIT IN PROCESS

In this paper we study the time complexities of some two‐ and three‐stage no‐wait flowshop makespan scheduling problems where, in some stage, all the jobs require a constant processing time and the stage may consist of parallel identical machines. Polynomial time algorithms are presented for certain problems, while several others are proved to be strongly NP‐complete.     

Inference for the generalized Rayleigh distribution based on progressively censored data

In this paper, and based on a progressive type-II censored sample from the generalized Rayleigh (GR) distribution, we consider the problem of estimating the model parameters and predicting the unobserved removed data. Maximum likelihood and Bayesian approaches are used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are used to predict the life lengths of the removed units in multiple stages of the progressively censored sample. Artificial and real data analyses have been performed for illustrative purposes.     

Combining least-squares and quantile regressions

Least-squares and quantile regressions are method of moments techniques that are typically used in isolation. A leading example where efficiency may be gained by combining least-squares and quantile regressions is one where some information on the error quantiles is available but the error distribution cannot be fully specified. This estimation problem may be cast in terms of solving an over-determined estimating equation (EE) system for which the generalized method of moments (GMM) and empirical likelihood (EL) are approaches of recognized importance. The major difficulty with implementing these techniques here is that the EEs associated with the quantiles are non-differentiable. In this paper, we develop a kernel-based smoothing technique for non-smooth EEs, and derive the asymptotic properties of the GMM and maximum smoothed EL (MSEL) estimators based on the smoothed EEs. Via a simulation study, we investigate the finite sample properties of the GMM and MSEL estimators that combine least-squares and quantile moment relationships. Applications to real datasets are also considered.     

A course for clinical trial personnel in clinical study designs, randomization, allocation schedules, and interactive response systems

This continuing education course for professionals involved in all areas of clinical trials integrates concepts related to the role of randomization in the scientific process. The course includes two interactive lecture and discussion sections and a workshop practicum. The first interactive lecture introduces basic clinical trial issues and statistical principles such as bias, blinding, randomization, control groups, and the importance of formulating clear and discriminating clinical and statistical hypotheses. It then focuses on the most commonly used clinical study designs and the corresponding patient randomization schemes. The second interactive lecture focuses on the implementation of randomization of patients and drug supply through allocation and component ID schedules. The workshop practicum, conducted in small groups, enables students to apply the lecture concepts to real clinical studies. Flexibility was built into the workshop practicum materials to allow the course content to be customized to specific audiences, and the interactive lecture sessions can be stretched to cover more advanced topics according to class interest and time availability.     

Welfare reforms and the Refugee Resettlement Strategy: an opportunity to achieve meaningful employment outcomes for New Zealanders from refugee backgrounds?

Despite employment being consistently identified as a key factor in successful refugee resettlement, people from refugee backgrounds in Aotearoa New Zealand are overrepresented in unemployment statistics. Of those who do gain employment, few secure work that is adequately remunerated and commensurate with the person's skills and qualifications. This paper explores whether the two recent government-driven initiatives, the welfare reforms and the New Zealand Refugee Resettlement Strategy, provide an opportunity to address these issues. Based on previous research, the authors identify the main employment barriers facing people from refugee backgrounds. They argue that while the welfare reforms and the Refugee Resettlement Strategy are underpinned by a desire to see more people in employment, for real change to occur, an integrated holistic approach is needed. This approach needs to include additional resourcing for government-funded specialist one-on-one employment programmes that are available in all regions where refugees are resettled. These programmes combined with access to fully funded English language tuition and work experience and internship opportunities would help reduce the barriers people from refugee backgrounds face when seeking employment.     

Extending the Mann–Whitney–Wilcoxon rank sum test to longitudinal regression analysis

Outliers are commonly observed in psychosocial research, generally resulting in biased estimates when comparing group differences using popular mean-based models such as the analysis of variance model. Rank-based methods such as the popular Mann–Whitney–Wilcoxon (MWW) rank sum test are more effective to address such outliers. However, available methods for inference are limited to cross-sectional data and cannot be applied to longitudinal studies under missing data. In this paper, we propose a generalized MWW test for comparing multiple groups with covariates within a longitudinal data setting, by utilizing the functional response models. Inference is based on a class of U-statistics-based weighted generalized estimating equations, providing consistent and asymptotically normal estimates not only under complete but missing data as well. The proposed approach is illustrated with both real and simulated study data.     

Asymptotic Comparison Between Constant-stress Testing and Step-stress Testing for Type-I Censored Data from Exponential Distribution

By running the life tests at higher stress levels than normal operating conditions, accelerated life testing quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant-stress testing, a unit is tested at a fixed stress level until failure or the termination time point of the test, while step-stress testing allows the experimenter to gradually increase the stress levels at some pre-fixed time points during the test. In this article, the optimal k-level constant-stress and step-stress accelerated life tests are compared for the exponential failure data under Type-I censoring. The objective is to quantify the advantage of using the step-stress testing relative to the constant-stress one. A log-linear relationship between the mean lifetime parameter and stress level is assumed and the cumulative exposure model holds for the effect of changing stress in step-stress testing. The optimal design point is then determined under C-optimality, D-optimality, and A-optimality criteria. The efficiency of step-stress testing compared to constant-stress testing is discussed in terms of the ratio of optimal objective functions based on the information matrix.     

On Variational Bayes Estimation and Variational Information Criteria for Linear Regression Models

Variational Bayes (VB) estimation is a fast alternative to Markov Chain Monte Carlo for performing approximate Baesian inference. This procedure can be an efficient and effective means of analyzing large datasets. However, VB estimation is often criticised, typically on empirical grounds, for being unable to produce valid statistical inferences. In this article we refute this criticism for one of the simplest models where Bayesian inference is not analytically tractable, that is, the Bayesian linear model (for a particular choice of priors). We prove that under mild regularity conditions, VB based estimators enjoy some desirable frequentist properties such as consistency and can be used to obtain asymptotically valid standard errors. In addition to these results we introduce two VB information criteria: the variational Akaike information criterion and the variational Bayesian information criterion. We show that variational Akaike information criterion is asymptotically equivalent to the frequentist Akaike information criterion and that the variational Bayesian information criterion is first order equivalent to the Bayesian information criterion in linear regression. These results motivate the potential use of the variational information criteria for more complex models. We support our theoretical results with numerical examples.