A unified minimax result for restricted parameter spaces

We provide a development that unifies, simplifies and extends considerably a number of minimax results in the restricted parameter space literature. Various applications follow, such as that of estimating location or scale parameters under a lower (or upper) bound restriction, location parameter vectors restricted to a polyhedral cone, scale parameters subject to restricted ratios or products, linear combinations of restricted location parameters, location parameters bounded to an interval with unknown scale, quantiles for location-scale families with parametric restrictions and restricted covariance matrices.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ336 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On the behavior of Bayesian credible intervals for some restricted parameter space problems

For estimating a positive normal mean, Zhang and Woodroofe (2003) as well as Roe and Woodroofe (2000) investigate 100($1-\alpha)$ HPD credible sets associated with priors obtained as the truncation of noninformative priors onto the restricted parameter space. Namely, they establish the attractive lower bound of $\frac{1-\alpha}{1+\alpha}$ for the frequentist coverage probability of these procedures. In this work, we establish that the lower bound of $\frac{1-\alpha}{1+\alpha}$ is applicable for a substantially more general setting with underlying distributional symmetry, and obtain various other properties. The derivations are unified and are driven by the choice of a right Haar invariant prior. Investigations of non-symmetric models are carried out and similar results are obtained. Namely, (i) we show that the lower bound $\frac{1-\alpha}{1+\alpha}$ still applies for certain types of asymmetry (or skewness), and (ii) we extend results obtained by Zhang and Woodroofe (2002) for estimating the scale parameter of a Fisher distribution; which arises in estimating the ratio of variance components in a one-way balanced random effects ANOVA. Finally, various examples illustrating the wide scope of applications are expanded upon. Examples include estimating parameters in location models and location-scale models, estimating scale parameters in scale models, estimating linear combinations of location parameters such as differences, estimating ratios of scale parameters, and problems with non-independent observations.Comment: Published at http://dx.doi.org/10.1214/074921706000000635 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Self-Referential Thinking, Suicide, and Function of the Cortical Midline Structures and Striatum in Mood Disorders: Possible Implications for Treatment Studies of Mindfulness-Based Interventions for Bipolar Depression

Bipolar depression is often refractory to treatment and is frequently associated with anxiety symptoms and elevated suicide risk. There is a great need for adjunctive psychotherapeutic interventions. Treatments with effectiveness for depressive and anxiety symptoms as well as suicide-related thoughts and behaviors would be particularly beneficial. Mindfulness-based interventions hold promise, and studies of these approaches for bipolar disorder are warranted. The aim of this paper is to provide a conceptual background for such studies by reviewing key findings from diverse lines of investigation. Results of that review indicate that cortical midline structures (CMS) appear to link abnormal self-referential thinking to emotional dysregulation in mood disorders. Furthermore, CMS and striatal dysfunction may play a role in the neuropathology underlying suicide-related thoughts and behaviors. Thus, combining studies of mindfulness interventions targeting abnormal self-referential thinking with functional imaging of CMS and striatal function may help delineate the neurobiological mechanisms of action of these treatments

Ranking Inequality: Applications of Multivariate Subset Selection

Inequality measures are often presented in the form of a rank ordering to highlight their relative magnitudes. However, a rank ordering may produce misleading inference, because the inequality measures themselves are statistical estimators with different standard errors, and because a rank ordering necessarily implies multiple comparisons across all measures. Within this setting, if differences between several inequality measures are simultaneously and statistically insignificant, the interpretation of the ranking is changed. This study uses a multivariate subset selection procedure to make simultaneous distinctions across inequality measures at a pre-specified confidence level. Three applications of this procedure are explored using country-level data from the Luxembourg Income Study. The findings show that simultaneous precision plays an important role in relative inequality comparisons and should not be ignored.Income distribution, Inference, Poverty, Subset Selection

Stuck at home in a cold home: the implications of Covid-19 for the fuel poor

Policies to address the impact of Covid-19 on low income energy consumers have rightly focussed on energy bills, particularly in the context of home confinement and increased energy consumption. In the longer term, however, we need policies to improve home energy standards. The evidence shows that higher standards reduce the risk of getting a respiratory illness, improve the health of those already with a respiratory illness, improve the ability of our immune systems to fight off illness and reduce the use of health services

Aberrant functional connectivity of cortico-basal ganglia circuits in major depression

ManuscriptThere is considerable evidence of functional abnormalities of the cortico-basal ganglia circuitry in affective disorders. However, it has been unknown whether this represented primary pathology within these circuits or altered activation as a result of aberrant input from other brain regions. The aim of this study was to test the hypothesis that cortico-basal ganglia circuit dysfunction represents primary pathology in unipolar depression. Eighteen male subjects with recurrent unipolar depression and eighteen controls without psychiatric illness were studied using functional MRI and functional connectivity analyses. All unipolar subjects were unmedicated and without current psychiatric comorbidity. Compared to controls, unipolar subjects exhibited altered connectivity between bilateral subcortical components of the circuitry (putamen-thalamus) and left hemisphere input and output components. Results provided evidence that functional abnormalities of these circuits represent primary pathology. Further, we found that age of onset but not duration of illness impacts circuit function. These findings suggest that the cortico-basal ganglia circuitry is likely one of several loci of primary pathology in major depression. Additionally, early age of onset is associated with greater circuit abnormality and as such may impact clinical characteristics and/or treatment response through a mechanism of decreasing functional connectivity of some circuit segments. Finally, altered cortico-basal ganglia circuit connectivity with cortical regions (anterior cingulate, inferior frontal gyrus and sensorimotor) may contribute to the emotional dysregulation, impaired emotional recognition and psychomotor symptoms associated with unipolar illness