This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its “quality.” Identification can be regular or irregular, depending on whether the Fisher information for the parameter is positive or zero, respectively. I first characterize these cases in models with densities linear in an infinite-dimensional parameter. I then introduce a novel “generalized Fisher information.” If positive, it implies (possibly irregular) identification when other conditions hold. If zero, it implies impossibility results on rates of estimation. Three examples illustrate the applicability of the general results. First, I consider the canonical example of average densities. Second, I show irregular identification of the median willingness to pay in contingent valuation studies. Finally, I study identification of the discount factor and average measures of risk aversion in a nonparametric Euler equation with nonparametric measurement error in consumption.

The size-Ramsey number of a graph F is the smallest number of edges in a graph G with the Ramsey property for F, that is, with the property that any 2-colouring of the edges of G contains a monochromatic copy of F. We prove that the size-Ramsey number of the grid graph on n × n vertices is bounded from above by n3+o(1).

We revisit an old topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and ball-covering (metric entropy) measures. For some familiar models of random graphs, this connection allows the order of magnitude of the cover time to be deduced from first passage percolation estimates. Establishing sharper results seems a challenging problem.

Invasive meningococcal disease has high morbidity and mortality, with infants and young children among those at greatest risk. This phase III, open-label, randomised study in toddlers aged 12–23 months evaluated the immunogenicity and safety of meningococcal tetanus toxoid-conjugate vaccine (MenACYW-TT), a tetanus toxoid conjugated vaccine against meningococcal serogroups A, C, W and Y, when coadministered with paediatric vaccines (measles, mumps and rubella [MMR]; varicella [V]; 6-in-1 combination vaccine against diphtheria, tetanus, pertussis, polio, hepatitis B and Haemophilus influenzae type b [DTaP-IPV-HepB-Hib] and pneumococcal conjugate vaccine [PCV13])(NCT03205371). Immunogenicity to each meningococcal serogroup was assessed by serum bactericidal antibody assay using human complement (hSBA). Vaccine safety profiles were described up to 30 days post-vaccination. A total of 1183 participants were enrolled. The proportion with seroprotection (hSBA ≥1:8) to each meningococcal serogroup at Day 30 was comparable between the MenACYW-TT and MenACYW-TT + MMR + V groups (≥92 and ≥96%, respectively), between the MenACYW-TT and MenACYW-TT + DTaP-IPV-HepB-Hib groups (≥90% for both) and between the MenACYW-TT and MenACYW-TT + PCV13 groups (≥91 and ≥84%, respectively). The safety profiles of MenACYW-TT, and MMR + V, DTaP-IPV-HepB-Hib, and PCV13, with or without MenACYW-TT, were generally comparable. Coadministration of MenACYW-TT with paediatric vaccines in toddlers had no clinically relevant effect on the immunogenicity and safety of any of the vaccines.

Europe is in the midst of a COVID-19 epidemic and a number of non-pharmaceutical public health and social measures have been implemented, in order to contain the transmission of severe acute respiratory syndrome coronavirus 2. These measures are fundamental elements of the public health approach to controlling transmission but have proven not to be sufficiently effective. Therefore, the European Centre for Disease Prevention and Control has conducted an assessment of research gaps that can help inform policy decisions regarding the COVID-19 response. We have identified research gaps in the area of non-pharmaceutical measures, physical distancing, contact tracing, transmission, communication, mental health, seasonality and environment/climate, surveillance and behavioural aspects of COVID-19. This prioritisation exercise is a step towards the global efforts of developing a coherent research road map in coping with the current epidemic but also developing preparedness measures for the next unexpected epidemic.

In this paper, we present a method to estimate the risk of reopening of schools illustrated with the case of the State of São Paulo, Brazil. The model showed that, although no death of children would result from the reopening of the schools in the three cities analysed, the risk of asymptomatic and symptomatic cases and secondary cases among teachers, school staff and relatives of the children is not negligible. Although the epidemic hit different regions with different intensities, our model shows that, for regions where the incidence profile is similar to the cities analysed, the risk of reopening of schools is still too high. This in spite of the fact that incidences in these cities were declining in the period of the time considered. Therefore, although we cannot extend the result to the entire country, the overall conclusion is valid for regions with a declining incidence and it is even more valid for regions where incidence is increasing. We assumed a very conservative level of infection transmissibility of children of just 10% as that of adults. In spite of the very low level of transmissibility is assumed, the number of secondary cases caused by infected children among teachers, school staff and relatives varied from 2 to 85. It is, therefore, too soon to have any degree of confidence that reopening of schools before the advent of a vaccine is the right decision to take. The purpose of our model and simulations is to provide a method to estimate the risk of school reopening, although we are sure it could be applied as a guide to public health strategies.

The mvClaim package in R provides flexible modelling frameworks for multivariate insurance claim severity modelling. The current version of the package implements a parsimonious mixture of experts (MoE) model family with bivariate gamma distributions, as introduced in Hu et al., and a finite mixture of copula regressions within the MoE framework as in Hu & O’Hagan. This paper presents the modelling approach theory briefly and the usage of the models in the package in detail. This package is hosted on GitHub at https://github.com/senhu/.

Case identification is an ongoing issue for the COVID-19 epidemic, in particular for outpatient care where physicians must decide which patients to prioritise for further testing. This paper reports tools to classify patients based on symptom profiles based on 236 severe acute respiratory syndrome coronavirus 2 positive cases and 564 controls, accounting for the time course of illness using generalised multivariate logistic regression. Significant symptoms included abdominal pain, cough, diarrhoea, fever, headache, muscle ache, runny nose, sore throat, temperature between 37.5 and 37.9 °C and temperature above 38 °C, but their importance varied by day of illness at assessment. With a high percentile threshold for specificity at 0.95, the baseline model had reasonable sensitivity at 0.67. To further evaluate accuracy of model predictions, leave-one-out cross-validation confirmed high classification accuracy with an area under the receiver operating characteristic curve of 0.92. For the baseline model, sensitivity decreased to 0.56. External validation datasets reported similar result. Our study provides a tool to discern COVID-19 patients from controls using symptoms and day from illness onset with good predictive performance. It could be considered as a framework to complement laboratory testing in order to differentiate COVID-19 from other patients presenting with acute symptoms in outpatient care.

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a probabilistic, distance-based, iterative method for clustering data in very high-dimensional space, using the ℓ1-metric that is less sensitive to high dimensionality than the Euclidean distance. For K clusters in ℝn, the problem decomposes to K problems coupled by probabilities, and an iteration reduces to finding Kn weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.

We explore the tree limits recently defined by Elek and Tardos. In particular, we find tree limits for many classes of random trees. We give general theorems for three classes of conditional Galton–Watson trees and simply generated trees, for split trees and generalized split trees (as defined here), and for trees defined by a continuous-time branching process. These general results include, for example, random labelled trees, ordered trees, random recursive trees, preferential attachment trees, and binary search trees.

Renal Replacement Therapies generally associated to the Artificial Kidney (AK) are membrane-based treatments that assure the separation functions of the failing kidney in extracorporeal blood circulation. Their progress from conventional hemodialysis towards high-flux hemodialysis (HFHD) through the introduction of ultrafiltration membranes characterized by high convective permeation fluxes intensified the need of elucidating the effect of the membrane fluid removal rates on the increase of the potentially blood-traumatizing shear stresses developed adjacently to the membrane. The AK surrogate consisting of two-compartments separated by an ultrafiltration membrane is set to have water circulation in the upper chamber mimicking the blood flow rates and the membrane fluid removal rates typical of HFHD. Pressure drop mirrors the shear stresses quantification and the modification of the velocities profiles. The increase on pressure drop when comparing flows in slits with a permeable membrane and an impermeable wall is ca. 512% and 576% for $ \mathrm{CA}22/5\%{\mathrm{SiO}}_2 $ and $ \mathrm{CA}30/5\%{\mathrm{SiO}}_2 $ membranes, respectively.

Target date funds (TDFs) are becoming increasingly popular investment choices among investors with long-term prospects. Examples include members of superannuation funds seeking to save for retirement at a given age. TDFs provide efficient risk exposures to a diversified range of asset classes that dynamically match the risk profile of the investment payoff as the investors age. This is often achieved by making increasingly conservative asset allocations over time as the retirement date approaches. Such dynamically evolving allocation strategies for TDFs are often referred to as glide paths. We propose a systematic approach to the design of optimal TDF glide paths implied by retirement dates and risk preferences and construct the corresponding dynamic asset allocation strategy that delivers the optimal payoffs at minimal costs. The TDF strategies we propose are dynamic portfolios consisting of units of the growth-optimal portfolio (GP) and the risk-free asset. Here, the GP is often approximated by a well-diversified index of multiple risky assets. We backtest the TDF strategies with the historical returns of the S&P500 total return index serving as the GP approximation.

To assess the relationship between the neutrophil-to-lymphocyte ratio (NLR) and related parameters to the severity of coronavirus disease 2019 (COVID-19) symptoms. Clinical data from 38 COVID-19 patients who were diagnosed, treated and discharged from the Qishan Hospital in Yantai over the period from January to February 2020 were analysed. NLR and procalcitonin (PCT) were determined in the first and fourth weeks after their admission, along with the clinical characteristics and laboratory test results of these patients. Based on results as obtained on the first and fourth weeks after admission, five indices consisting of NLR, white blood cells, neutrophils, lymphocytes (LY) and monocytes (MON) were selected to generate receiver operating characteristic curves, while optimal cutoff values, sensitivities and specificities were obtained according to the Yuden index. Statistically significant differences in neutrophils, LY and the NLR were present in the severe vs. moderate COVID-19 group from the first to the fourth week of their hospitalisation. The cut-off value of NLR for predicting the severity of COVID-19 was 4.425, with a sensitivity of 0.855 and a specificity of 0.979. A statistically significant positive correlation was present between PCT and NLR in the severe group as determined within the first week of admission. NLR can serve as a predictor of COVID-19 disease severity as patients' progress from the first to the fourth week of their hospitalisation. The statistically significant positive correlation between levels of NLR and PCT in severe patients indicated that increases in NLR were accompanied with gradual increases in PCT.

In this paper, the optimal insurance design is studied from the perspective of an insured, who faces an insurable risk and a background risk. For the reduction of ex post moral hazard, alternative insurance contracts are asked to satisfy the principle of indemnity and the incentive-compatible condition. As in the literature, it is assumed that the insurer calculates the insurance premium solely on the basis of the expected indemnity. When the insured has a general mean-variance preference, an explicit form of optimal insurance is derived explicitly. It is found that the stochastic dependence between the background risk and the insurable risk plays a critical role in the insured’s risk transfer decision. In addition, the optimal insurance policy can often change significantly once the incentive-compatible constraint is removed.

This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.

The current investigation was conducted with the objective to develop an epidemiological case definition of possible severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) re-infection and assess its magnitude in India. The epidemiological case definition for SARS-CoV-2 re-infection was developed from literature review of data on viral kinetics. For achieving second objective, the individuals who satisfied the developed case definition for SARS-CoV-2 re-infection were contacted telephonically. Taking available evidence into consideration, re-infection with SARS-CoV-2 in our study was defined as any individual who tested positive for SARS-CoV-2 on two separate occasions by either molecular tests or rapid antigen test at an interval of at least 102 days with one negative molecular test in between. In this archive based, telephonic survey, 58 out of 1300 individuals (4.5%) fulfilled the above-mentioned definition; 38 individuals could be contacted with healthcare workers (HCWs) accounting for 31.6% of the cases. A large proportion of participants was asymptomatic and had higher Ct value during the first episode. While SARS-CoV-2 re-infection is still a rare phenomenon, there is a need for epidemiological definition of re-infection for establishing surveillance systems and this study contributes to such a goal.

Severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) re-infection is an emerging concern and there is a need to define it. Therefore, working epidemiological case definition for re-infection was developed and its magnitude was explored via archive-based, telephonic survey. Re-infection with SARS-CoV-2 was defined as two positive tests at an interval of at least 102 days with one interim negative test. Thirty-eight of the 58 eligible patients could be contacted with 12 (31.6%) being HCWs. Majority of the participants were asymptomatic and had higher Ct value during their first episode. To conclude, a working epidemiological case definition of SARS-CoV-2 re-infection is important to strengthen surveillance. The present investigation contributes to this goal and records reinfection in 4.5% of SARS-CoV-2 infected individuals in India.