Confidence Corridors for Multivariate Generalized Quantile Regression

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem and exponential tail inequalities for Gaussian random fields. As a byproduct we also obtain confidence corridors for the regression function in the classical mean regression. In order to deal with the problem of slowly decreasing error in coverage probability of the asymptotic confidence corridors, which results in meager coverage for small sample sizes, a simple bootstrap procedure is designed based on the leading term of the Bahadur representation. The finite sample properties of both procedures are investigated by means of a simulation study and it is demonstrated that the bootstrap procedure considerably outperforms the asymptotic bands in terms of coverage accuracy. Finally, the bootstrap confidence corridors are used to study the efficacy of the National Supported Work Demonstration, which is a randomized employment enhancement program launched in the 1970s. This article has supplementary materials

Quantile Regression in Risk Calibration

Financial risk control has always been challenging and becomes now an even harder problem as joint extreme events occur more frequently. For decision makers and government regulators, it is therefore important to obtain accurate information on the interdependency of risk factors. Given a stressful situation for one market participant, one likes to measure how this stress affects other factors. The CoVaR (Conditional VaR) framework has been developed for this purpose. The basic technical elements of CoVaR estimation are two levels of quantile regression: one on market risk factors; another on individual risk factor. Tests on the functional form of the two-level quantile regression reject the linearity. A flexible semiparametric modeling framework for CoVaR is proposed. A partial linear model (PLM) is analyzed. In applying the technology to stock data covering the crisis period, the PLM outperforms in the crisis time, with the justification of the backtesting procedures. Moreover, using the data on global stock markets indices, the analysis on marginal contribution of risk (MCR) defined as the local first order derivative of the quantile curve sheds some light on the source of the global market risk.CoVaR, Value-at-Risk, quantile regression, locally linear quantile regression, partial linear model, semiparametric model

Distributed Bootstrap for Simultaneous Inference Under High Dimensionality

We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces a $\ell_\infty$-norm confidence region based on a communication-efficient de-biased lasso, and we propose an efficient cross-validation approach to tune the method at every iteration. We theoretically prove a lower bound on the number of communication rounds $\tau_{\min}$ that warrants the statistical accuracy and efficiency. Furthermore, $\tau_{\min}$ only increases logarithmically with the number of workers and intrinsic dimensionality, while nearly invariant to the nominal dimensionality. We test our theory by extensive simulation studies, and a variable screening task on a semi-synthetic dataset based on the US Airline On-time Performance dataset. The code to reproduce the numerical results is available at GitHub: https://github.com/skchao74/Distributed-bootstrap.Comment: arXiv admin note: text overlap with arXiv:2002.0844

Characteristics of human immunodeficiency virus infections among the elderly in Taiwan: A nationwide study

AbstractBackgroundInformation regarding human immunodeficiency virus (HIV) infections and acquired immunodeficiency syndrome (AIDS) in the elderly of Taiwan is limited. This study looked into the aforementioned issues.MethodsData from the National HIV/AIDS Registry, relating to individuals diagnosed in 2007, were analyzed.ResultsAmong 1,975 HIV-infected individuals diagnosed in 2007, the elderly group (age ≧50 years) consisted of 153 subjects and the younger (control) group (age 15–39 years) consisted of 1,458 individuals. Some markers, such as primarily males/local Taiwanese, being unemployed, one third of subjects infected by means of intravenous drug use, and primarily diagnosed in hospitals, were similar between the two groups. The elderly group had more married, divorced, and separated individuals, and widows/widowers than the younger group. The causes of death differed insignificantly between the two groups. The younger group had more variety than the elderly group in distribution of occupations. Fewer prison-diagnosed HIV, high ratio of individuals developing AIDS, heterosexuals, high mortality, and unsupported marital status were significant markers of elderly HIV-infected subjects.ConclusionIn Taiwan, elderly HIV infections have reflected the aforementioned characteristics. Some specific issues concerning elderly HIV infections, such as heterosexual predominance, high mortality and fewer men who have sex with men, are similar with reports from other countries. These characteristics can guide possible directions of social and health care interventions

The utilization of hospice care among patients with motor neuron diseases: The experience in Taiwan from 2005 to 2010

AbstractBackgroundThe nature and extent of how patients with motor neuron diseases (MNDs) utilize hospice care in Taiwan remains unclear. This study aims to investigate the use of hospice care in Taiwan by patients with MND, and those factors that affect the extent, the cost, and the quality of their hospice treatment and care.MethodsWe analyzed data from hospice care inpatient claims of MNDs, using the National Health Insurance Research Database of Taiwan during 2005–2010.ResultsThirty patients and 58 related discharges were enrolled into our study, which consisted of 13 males and 17 females, with a mean age 58.3 years. Of that total, 27 of them (90%) had amyotrophic lateral sclerosis, and four (13.3%) had comorbid cancers; 17 died during hospice care. Acute low respiratory conditions (31.0%) accounted for the most common acute comorbidity. Noninvasive ventilation care was performed in only 13 (22.4%) of the discharges. In contrast to nasogastric intubation (40 discharges, 69.0%), no gastrostomy/jejunostomy was noted. These procedures bore no relationship to results observed in the discharges. Family physicians provided most inpatient hospice services (74.1%). Respiratory problems were the major causes of death (70.6% of decedents). The mean inpatient costs of hospice care were noticeably reduced from previously established nationwide mean costs.ConclusionHospice care can save costs for patients with terminal MNDs, and family physicians play a valuable role in caring for these patients. However, respiratory and feeding problems are prevalent, yet there are proven benefits when noninvasive ventilation care and gastrostomy/jejunostomy are promoted