Gromov–Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures living on Euclidean spaces of different dimensions. We focus on the Gromov–Wasserstein distance with a ground cost defined as the squared Euclidean distance, and we study the form of the optimal plan between Gaussian distributions. We show that when the optimal plan is restricted to Gaussian distributions, the problem has a very simple linear solution, which is also a solution of the linear Gromov–Monge problem. We also study the problem without restriction on the optimal plan, and provide lower and upper bounds for the value of the Gromov–Wasserstein distance between Gaussian distributions.

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other fixed-effect models for panel data. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias in the empirical distribution arising from the presence of noise. The leading bias in the empirical quantile function is equally obtained. These calculations are new in the literature, where only results on smooth functionals such as the mean and variance have been derived. We provide both analytical and jackknife corrections that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. Our approach can be connected to corrections for selection bias and shrinkage estimation and is to be contrasted with deconvolution. Simulation results confirm the much-improved sampling behavior of the corrected estimators. An empirical illustration on heterogeneity in deviations from the law of one price is equally provided.

In this paper we revisit some classical queueing systems such as the M$^b$/E$_k$/1/m and E$_k$/M$^b$/1/m queues, for which fast numerical and recursive methods exist to study their main performance measures. We present simple explicit results for the loss probability and queue length distribution of these queueing systems as well as for some related queues such as the M$^b$/D/1/m queue, the D/M$^b$/1/m queue, and fluid versions thereof. In order to establish these results we first present a simple analytical solution for the invariant measure of the M/E$_k$/1 queue that appears to be new.

This paper considers the estimation of panel data models with interactive fixed effects where the idiosyncratic errors are subject to conditional quantile restrictions. An easy-to-implement two-step estimator is proposed for the coefficients of the observed regressors. In the first step, the principal component analysis is applied to the cross-sectional averages of the regressors to estimate the latent factors. In the second step, the smoothed quantile regression is used to estimate the coefficients of the observed regressors and the factor loadings jointly. The consistency and asymptotic normality of the estimator are established under large $N,T$ asymptotics. It is found that the asymptotic distribution of the estimator suffers from asymptotic biases, and this paper shows how to correct the biases using both analytical and split-panel jackknife bias corrections. Simulation studies confirm that the proposed estimator performs well with moderate sample sizes.

The Dagum family of isotropic covariance functions has two parameters that allow for decoupling of the fractal dimension and the Hurst effect for Gaussian random fields that are stationary and isotropic over Euclidean spaces. Sufficient conditions that allow for positive definiteness in $\mathbb{R}^d$ of the Dagum family have been proposed on the basis of the fact that the Dagum family allows for complete monotonicity under some parameter restrictions. The spectral properties of the Dagum family have been inspected to a very limited extent only, and this paper gives insight into this direction. Specifically, we study finite and asymptotic properties of the isotropic spectral density (intended as the Hankel transform) of the Dagum model. Also, we establish some closed-form expressions for the Dagum spectral density in terms of the Fox–Wright functions. Finally, we provide asymptotic properties for such a class of spectral densities.

Symptoms are currently used as testing indicators for SARS-CoV-2 in England. In this study, we analysed national contact tracing data for England (NHS Test and Trace) for the period 1 December to 28 December 2021 to explore symptom differences between the variants, Delta and Omicron. We found that at least one of the symptoms currently used as indicators (fever, cough and loss of smell and taste) were reported in 61.5% of Omicron cases and 72.2% in Delta cases, suggesting that these symptoms are less predictive of Omicron infections. Nearly 40% of Omicron infections did not report any of the three key indicative symptoms, reinforcing the importance of the entire spectrum of symptoms for targeted testing. After adjusting for potential confounding factors, fever and cough were more commonly associated with Omicron infections compared to Delta, showing the importance of considering age and vaccination status when assessing symptom profiles. Sore throat was also more commonly reported in Omicron infections, and loss of smell and taste more commonly reported in Delta infections. Our study shows the value of continued monitoring of symptoms associated with SARS-CoV-2, as changes may influence the effectiveness of testing policy and case ascertainment approaches.

Patient-important outcomes related to coronavirus disease 2019 (COVID-19) continue to drive the pandemic response across the globe. Various prognostic factors for COVID-19 severity have emerged and their replication across different clinical settings providing health services is ongoing. We aimed to describe the clinical characteristics and their association with outcomes in patients hospitalised with COVID-19 in the University Hospital of Ioannina. We assessed a cohort of 681 consecutively hospitalised patients with COVID-19 from January 2020 to December 2021. Demographic data, underlying comorbidities, clinical presentation, biochemical markers, radiologic findings, COVID-19 treatment and outcome data were collected at the first day of hospitalisation and up to 90 days. Multivariable Cox regression analyses were performed to investigate the associations between clinical characteristics (hazard ratios (HRs) per standard deviation (s.d.)) with intubation and/or mortality status. The participants' mean age was 62.8 (s.d., 16.9) years and 57% were males. The most common comorbidities were hypertension (45%), cardiovascular disease (19%) and diabetes mellitus (21%). Patients usually presented with fever (81%), cough (50%) and dyspnoea (27%), while lymphopenia and increased inflammatory markers were the most common laboratory abnormalities. Overall, 55 patients (8%) were intubated, and 86 patients (13%) died. There were statistically significant positive associations between intubation or death with age (HR: 2.59; 95% CI 1.52–4.40), lactate dehydrogenase (HR: 1.44; 95% CI 1.04–1.98), pO2/FiO2 ratio < 100 mmHg (HR: 3.52; 95% CI 1.14–10.84), and inverse association with absolute lymphocyte count (HR: 0.54; 95% CI 0.33–0.87). These data might help to identify points for improvement in the management of COVID-19 patients.

Healthcare-associated infection (HAI) is a major cause of morbidity, mortality and cost, which vary widely by region and hospital. In this case-control study, we calculated losses attributable to HAI in central China. A total of 2976 patients in 10 hospitals were enrolled, and the incidence rate of HAI (range, 0.88–4.15%) was significantly, but negatively associated with the cost per 1000 beds of its prevention (range, $24 929.76–$53 146.41; r = −0.76). The per capita economic loss attributable to HAIs was $2047.07 (interquartile range, $327.63–$6429.17), mainly from the pharmaceutical cost (median, $1044.39). The HAIs, which occurred in patients with commercial medical insurance, affected the haematologic system and caused by Acinetobacter baumannii, contributed most to the losses (median, $3881.55, $4734.20 and $9882.75, respectively). Furthermore, the economic losses attributable to device-associated infections and hospital-acquired multi-drug resistant bacteria were two to four times those of the controls. The burden attributable to HAI is heavy, and opportunities for easing this burden exist in several areas, including that strengthening antibiotic stewardship and practicing effective bundle of HAI prevention for patients carrying high-risk factors, for example, elders or those with catheterisations in healthcare institutions, and accelerating the medical insurance payment system reform based on diagnosis-related groups by policy-making departments.

In contrast to previous belief, we provide examples of stationary ergodic random measures that are both hyperfluctuating and strongly rigid. Therefore we study hyperplane intersection processes (HIPs) that are formed by the vertices of Poisson hyperplane tessellations. These HIPs are known to be hyperfluctuating, that is, the variance of the number of points in a bounded observation window grows faster than the size of the window. Here we show that the HIPs exhibit a particularly strong rigidity property. For any bounded Borel set B, an exponentially small (bounded) stopping set suffices to reconstruct the position of all points in B and, in fact, all hyperplanes intersecting B. Therefore the random measures supported by the hyperplane intersections of arbitrary (but fixed) dimension, are also hyperfluctuating. Our examples aid the search for relations between correlations, density fluctuations, and rigidity properties.

We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations. We give sufficient conditions on the degree sequence which guarantee existence of a solution to this system. Furthermore, we solve the system and give an explicit asymptotic formula when the degree sequence is close to regular. This allows us to establish several properties of the degree sequence of a random $r$-uniform hypergraph with a given number of edges. More specifically, we compare the degree sequence of a random $r$-uniform hypergraph with a given number edges to certain models involving sequences of binomial or hypergeometric random variables conditioned on their sum.

Human immunodeficiency virus (HIV) has been widely prevalent among older men (aged ≥50 years old) in Sichuan Province. The study aimed to discover associated factors with the new HIV infection in older men, and provide a scientific basis for the prevention and control of acquired immunodeficiency syndrome (AIDS) in this group. A cross-sectional survey study of newly reported HIV/AIDS and general male residents aged 50 years and older was conducted between April and June 2019, with a resample of respondents to identify cases and controls, followed by a case–control study. Logistic regression was applied to analyse the association between the selected factors and new HIV infection among older men. At last, 242 cases and 968 controls were included. The results of multiple logistic regression suggested that many factors including living alone/concentrated (OR 1.56, 95% CI 1.20–2.04, P = 0.001), have a history of migrant worker (OR 2.10, 95% CI 1.61–2.73, P < 0.001), have commercial sexual behaviour (OR 1.71, 95% CI 1.32–2.22, P < 0.001), married (OR 0.48, 95% CI 0.37–0.64, P < 0.001), have a history of HIV antibody testing (OR 0.73, 95% CI 0.56–0.96, P = 0.026), HIV-related knowledge (OR 0.55, 95% CI 0.42–0.72, P < 0.001) were associated with new HIV infection among older men. The present study revealed some potential risky/protective factors altogether. The results highlighted the direction of HIV/AIDS prevention and control among older men, and it is a social issue that requires the joint participation of the whole society.

In this paper we introduce new birth-and-death processes with partial catastrophe and study some of their properties. In particular, we obtain some estimates for the mean catastrophe time, and the first and second moments of the distribution of the process at a fixed time t. This is completed by some asymptotic results.

The financing of long-term care and the planning of care capacity are of increasing interest due to demographic changes and the ageing population in many countries. Since many care-intensive conditions begin to manifest at higher ages, a better understanding and assessment of the expected costs, required infrastructure, and number of qualified personnel are essential. To evaluate the overall burden of institutional care, we derive a model based on the duration of stay in dependence and the intensity of help provided to elderly individuals. This article aims to model both aspects using novel longitudinal data from nursing homes in the canton of Geneva in Switzerland. Our data contain comprehensive health and care information, including medical diagnoses, levels of dependence, and physical and psychological impairments on 21,758 individuals. We build an accelerated failure time model to study the influence of selected factors on the duration of care and a beta regression model to describe the intensity of care. We show that apart from age and gender, the duration of stay before death is mainly affected by the underlying diseases and the number of different diagnoses. Simultaneously, care intensity is driven by the individual level of dependence and specific limitations. Using both evaluations, we approximate the overall care severity for individual profiles. Our study sheds light on the relevant medical, physical, and psychological health indicators that need to be accounted for, not only by care providers but also by policy-makers and insurers.

Let $q\ge2$ be an integer, $\{X_n\}_{n\geq 1}$ a stochastic process with state space $\{0,\ldots,q-1\}$, and F the cumulative distribution function (CDF) of $\sum_{n=1}^\infty X_n q^{-n}$. We show that stationarity of $\{X_n\}_{n\geq 1}$ is equivalent to a functional equation obeyed by F, and use this to characterize the characteristic function of X and the structure of F in terms of its Lebesgue decomposition. More precisely, while the absolutely continuous component of F can only be the uniform distribution on the unit interval, its discrete component can only be a countable convex combination of certain explicitly computable CDFs for probability distributions with finite support. We also show that $\mathrm{d} F$ is a Rajchman measure if and only if F is the uniform CDF on [0, 1].

Statistical learning—the skill to pick up probability-based regularities of the environment—plays a crucial role in adapting to the environment and learning perceptual, motor, and language skills in healthy and clinical populations. Here, we developed a new method to measure statistical learning without any manual responses. We used the Alternating Serial Reaction Time (ASRT) task, adapted to eye-tracker, which, besides measuring reaction times (RTs), enabled us to track learning-dependent anticipatory eye movements. We found robust, interference-resistant learning on RT; moreover, learning-dependent anticipatory eye movements were even more sensitive measures of statistical learning on this task. Our method provides a way to apply the widely used ASRT task to operationalize statistical learning in clinical populations where the use of manual tasks is hindered, such as in Parkinson’s disease. Furthermore, it also enables future basic research to use a more sensitive version of this task to measure predictive processing.

In this paper, we extend the optimal dividend and capital injection problem with affine penalty at ruin in (Xu, R. & Woo, J.K. (2020). Insurance: Mathematics and Economics 92: 1–16) to the case with singular dividend payments. The asymptotic relationships between our value function to the one with bounded dividend density are studied, which also help to verify that our value function is a viscosity solution to the associated Hamilton–Jacob–Bellman Quasi-Variational Inequality (HJBQVI). We also show that the value function is the smallest viscosity supersolution within certain functional class. A modified comparison principle is proved to guarantee the uniqueness of the value function as the viscosity solution within the same functional class. Finally, a band-type dividend and capital injection strategy is constructed based on four crucial sets; and the optimality of such band-type strategy is proved by using fixed point argument. Numerical examples of the optimal band-type strategies are provided at the end when the claim size follows exponential and gamma distribution, respectively.

Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.

We recently described a simple model through which we assessed what effect subjecting travellers to a single on-arrival test might have on reducing risk of importing disease cases during simulated outbreaks of coronavirus disease 2019 (COVID-19), influenza, severe acute respiratory syndrome (SARS) and Ebola. We build upon this work to allow for the additional requirement that inbound travellers also undergo a period of self-isolation upon arrival, where upon completion the traveller is again tested for signs of infection prior to admission across the border. Prior results indicated that a single on-arrival test has the potential to detect 9% of travellers infected with COVID-19, compared to 35%, 10% and 3% for travellers infected with influenza, SARS and Ebola, respectively. Our extended model shows that testing administered after a 2-day isolation period could detect up to 41%, 97%, 44% and 15% of COVID-19, influenza, SARS and Ebola infected travellers, respectively. Longer self-isolation periods increase detection rates further, with an 8-day self-isolation period suggesting detection rates of up to 94%, 100%, 98% and 62% for travellers infected with COVID-19, influenza, SARS and Ebola, respectively. These results therefore suggest that testing arrivals after an enforced period of self-isolation may present a reasonable method of protecting against case importation during international outbreaks.

We study the quasi-stationary behavior of the birth–death process with an entrance boundary at infinity. We give by the h-transform an alternative and simpler proof for the exponential convergence of conditioned distributions to a unique quasi-stationary distribution in the total variation norm. In addition, we also show that starting from any initial distribution the conditional probability converges to the unique quasi-stationary distribution exponentially fast in the $\psi$-norm.

We examined the possible sex and age differences in the proportion of experienced Coronavirus Disease 2019 (COVID-19) symptoms in unaware (previously) infected adults, and their uninfected counterparts, estimated by serostatus prior to vaccination, at the end of 2020 (Wuhan strain). A cross-sectional community-based study using a convenience sample of 10 001 adult inhabitants of a southern Dutch province, heavily affected by COVID-19, was conducted. Participants donated a blood sample to indicate past infection by serostatus (positive/negative). Experienced symptoms were assessed by questionnaire, before the availability of the serological test result. Only participants without confirmed SARS-CoV-2 infection were included (n = 9715, age range 18–90 years). The seroprevalence was comparable between men (17.3%) and women (18.0%), and participants aged 18–60 years (17.3%) and aged 60 years and older (18.6%). We showed sex and age differences in the proportion experienced symptoms by serostatus in a large cohort of both unaware (untested) seropositive compared with seronegative reference participants. Irritability only differed by serostatus in men (independent of age), while stomach ache, nausea and dizziness only differed by serostatus in women aged 60 years and older. Besides, the proportion of experiencing pain when breathing and headache differed by serostatus in men aged 18–60 years only. Our study highlights the importance of taking possible sex and age differences into account with respect to acute and long-term COVID-19 outcomes. Identifying symptom profiles for sex and age subgroups can contribute to timely identification of infection, gaining importance once governments currently move away from mass testing again.