Decomposition of Scatter Ratios Used in Monitoring Multivariate Process Variability

Wilks’ ratio statistic can be defined in terms of the ratio of the sample generalized variances of two non-independent estimators of the same covariance matrix. Recently this statistic has been proposed as a control statistic for monitoring changes in the covariance matrix of a multivariate normal process in a Phase II situation, particularly when the dimension is larger than the sample size. In this article we derive a technique for decomposing Wilks’ ratio statistic into the product of independent factors that can be associated with the components of the covariance matrix. With these results, we demonstrate that, when a signal is detected in a control procedure for the Phase II monitoring of process variability using the ratio statistic, the signaling value can be decomposed and the process variables contributing to the signal can be specifically identified.     

Detection and Interpretation of a Multivariate Signal Using Combined Charts

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.     

Re-examining two tests for bivariate normality

Many goodness of fit tests for bivariate normality are not rigorous procedures because the distributions of the proposed statistics are unknown or too difficult to manipulate. Two familiar examples are the ring test and the line test. In both tests the statistic utilized generally is approximated by a chi-square distribution rather than compared to its known beta distribution. These two procedures are re-examined and re-evaluated in this paper. It is shown that the chi-square approximation can be too conservative and can lead to unnecessary

rejection of normality.     

Moment properties of estimators for a type 1 extreme-value regression model

A regression model is considered in which the response variable has a type 1 extreme-value distribution for smallest values. Bias approximations for the maximum likelihood estimators are pivm and a bias reduction estimator for the scale parameter is proposed. The small sample moment properties of the maximum likelihood estimators are compared with the properties of the ordinary least squares estimators and the best linear unbiased estimators based on order statistics for grouped data.     

Legal Ruralism and California Parole Hearings: Space,Place, and the Carceral Landscape*

This article discusses the important relationship between rurality and criminal justice processes, drawing on field observations and in-depth interviews with parole commissioners to argue that California's physical carceral landscape profoundly shapes lifer parole hearings. First, commissioners report that prisons' location in rural areas affects the rehabilitative resources available, which are seen as an important aspect of their readiness for release. Location and perceived rurality of prisons shape commissioners' perception of the inmates at various institutions, creating implicitly different standards for inmates housed at different prisons. Second, spatiality and rurality influence parole commissioners' work lives, exacting a toll that includes onerous travel, early burnout, and challenges to assembling a diverse board. Together, these findings underscore the importance of legal ruralism to the relationship between spatial and carceral landscapes.     

Socioeconomic inequality and adjustments in children’s perceptions of their agency as they age in South Korea

This paper explores how children's perceptions of their agency, as something that is closely associated with its exercise, appear in relation to social structural factors, especially their socioeconomic positions, as they age. Using data from 862 10–18 years old in South Korea, we examine how children's expressed optimism about their ability to achieve their occupational choices can conceal the impact of structural factors on their ‘choices’ and dispositions for (non‐)action over time. Based on the findings, we argue for a more careful interpretation of children's sense of agency that recognises its propensity to continuously adjust in contexts of structural inequality.