A Necessary Condition for the Strong Oracle Property

A problem of using a non‐convex penalty for sparse regression is that there are multiple local minima of the penalized sum of squared residuals, and it is not known which one is a good estimator. The aim of this paper is to give a guide to design a non‐convex penalty that has the strong oracle property. Here, the strong oracle property means that the oracle estimator is the unique local minimum of the objective function. We summarize three definitions of the oracle property – the global, weak and strong oracle properties. Then, we give sufficient conditions for the weak oracle property, which means that the oracle estimator becomes a local minimum. We give an example of non‐convex penalties that possess the weak oracle property but not the strong oracle property. Finally, we give a necessary condition for the strong oracle property.     

Visualization for Large‐scale Gaussian Updates

In geostatistics and also in other applications in science and engineering, it is now common to perform updates on Gaussian process models with many thousands or even millions of components. These large‐scale inferences involve modelling, representational and computational challenges. We describe a visualization tool for large‐scale Gaussian updates, the ‘medal plot’. The medal plot shows the updated uncertainty at each observation location and also summarizes the sharing of information across observations, as a proxy for the sharing of information across the state vector (or latent process). As such, it reflects characteristics of both the observations and the statistical model. We illustrate with an application to assess mass trends in the Antarctic Ice Sheet, for which there are strong constraints from the observations and the physics.     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.     

Functional Partial Linear Single‐index Model

This paper deals with the problem of predicting the real‐valued response variable using explanatory variables containing both multivariate random variable and random curve. The proposed functional partial linear single‐index model treats the multivariate random variable as linear part and the random curve as functional single‐index part, respectively. To estimate the non‐parametric link function, the functional single‐index and the parameters in the linear part, a two‐stage estimation procedure is proposed. Compared with existing semi‐parametric methods, the proposed approach requires no initial estimation and iteration. Asymptotical properties are established for both the parameters in the linear part and the functional single‐index. The convergence rate for the non‐parametric link function is also given. In addition, asymptotical normality of the error variance is obtained that facilitates the construction of confidence region and hypothesis testing for the unknown parameter. Numerical experiments including simulation studies and a real‐data analysis are conducted to evaluate the empirical performance of the proposed method.     

Checking validity of monotone domain mean estimators

Estimates of population characteristics such as domain means are often expected to follow monotonicity assumptions. Recently, a method to adaptively pool neighbouring domains was proposed, which ensures that the resulting domain mean estimates follow monotone constraints. The method leads to asymptotically valid estimation and inference, and can lead to substantial improvements in efficiency, in comparison with unconstrained domain estimators. However, assuming incorrect shape constraints may lead to biased estimators. Here, we develop the Cone Information Criterion for Survey Data as a diagnostic method to measure monotonicity departures on population domain means. We show that the criterion leads to a consistent methodology that makes an asymptotically correct decision choosing between unconstrained and constrained domain mean estimators. The Canadian Journal of Statistics 47: 315–331; 2019 © 2019 Statistical Society of Canada     

Maternal Postpartum Depression Increases Vulnerability for Toddler Behavior Problems through Infant Cortisol Reactivity

The current study examined the role of hypothalamic‐pituitary‐adrenal reactivity (a physiological indicator of stress) in early infancy as a mediator of the relationship between maternal postpartum depression and toddler behavior problems. Participants were 137 at‐risk mothers and their children participating in a longitudinal study of intergenerational transmission of risk. Mothers’ depression was measured five times during the infants’ first 18 months. Infant cortisol was collected during a social stressor (the still‐face paradigm) when infants were 6 months old, and mothers reported on toddlers’ internalizing and externalizing symptoms at 18 months. Among this sample of high‐risk mother–infant dyads, early postpartum depression predicted atypical infant cortisol reactivity at 6 months, which mediated the effect of maternal depression on increased toddler behavior problems. Clinical implications are discussed.     

The Importance of Racial Socialization: School‐Based Racial Discrimination and Racial Identity Among African American Adolescent Boys and Girls

This study examined various parental racial socialization messages as mediators between school‐based racial discrimination and racial identity formation over 4 years for African American boys (N = 639) and African American girls (N = 711). Findings indicated that school‐based racial discrimination was associated with racial identity beliefs. For African American boys, behavioral racial socialization messages mediated the relation between school‐based racial discrimination and racial centrality over time. Mediation also resulted for African American girls, but for a different set of race‐related messages (negative messages and racial barriers) and racial identity beliefs. The developmental significance of the findings and implications for future research are discussed.     

The belonging model of trust

Although we know that high‐quality employee–organization relationships are beneficial, these relationships are complex and not fully understood, especially among employees of nonprofit organizations. In particular, we know little about how these employees perceive trust, which may overlook an important contributor to effective management. We begin to address this issue by testing a new theoretical model that conceptualizes perceived insider status, psychological ownership, and organizational identification as foundations for the perception of justice and subsequent trust. Our results indicate that psychological ownership and perceived insider status relate to trust through procedural and interpersonal justice. These results contrast those typically found in for‐profit contexts in that organizational identification did not predict justice and that distributive and informational justice did not predict trust.