Risk capital allocation refers to the problem of disaggregating the total capital requirement of a complex organization, such as a financial or insurance company, into additive contributions from its various units. The capital shares corresponding to each unit can be viewed as quantitative descriptions of the components of a whole, subject to a fixed sum constraint (full allocation). This interpretation suggests interesting connections between capital allocation principles and Compositional Data (CoDa) analysis. Prioritizing the compositional perspective, we propose a new optimality criterion for proportional risk capital allocations in insurance contexts. Our criterion requires that capital shares assigned to individual units should be “sufficiently close” to the corresponding loss proportions in a metric that is compatible with the Aitchison distance on the simplex. We solve this optimization problem under risk scenarios aligned with managerial concerns at the corporate level and we study the behavior of the resulting compositional allocations in alternative situations, reflecting different distributional assumptions and dependencies among risks. The outcomes of our numerical studies, including an empirical application to a public database of cyber-related losses, suggest that compositional risk capital allocations can offer a valuable alternative to traditional methods, particularly in scenarios involving heavy-tailed risks or requiring flexible allocation rules based on proportional rather then absolute contributions from the various risk sources.

Mediation analysis seeks to determine whether an independent variable affects a response directly or whether it does so indirectly, by way of a mediator or mediators. Scenarios that assume a single mediation are often overly simplistic, and analyses that include multiple mediators are becoming more common, particularly with the incorporation of high-dimensional data. Surprisingly, however, little attention has been given to multiple mediator and interaction effects. In this article, we propose new methods for testing the null hypothesis of no indirect effect with multiple mediators and interaction effects. We allow the estimators of the path effects to be possibly correlated; we also consider the practice of using confidence intervals to determine whether a mediation effect is zero. We compare the performance of our proposed method with existing methods through extensive simulation studies. Finally, we provide an application to data from the Coronary Artery Risk Development in Young Adults (CARDIA) study.

The nonparametric multivariate analysis of variance (NPMANOVA) testing procedure has been proven to be a valuable tool for comparing groups. In the present paper, we propose a kernel extension of this technique in order to effectively confront high-dimensionality, a recurrent problem in many fields of science. The new method is called kernel multivariate analysis of variance (KMANOVA). The basic idea is to take advantage of the kernel framework: we propose to project the data from the original data space to a Hilbert space generated by a given kernel function and then perform the NPMANOVA method in the reproducing kernel Hilbert space (RKHS). Dispersion of the embedded points can be measured by the distance induced by the inner product in the RKHS but also by many other distances best suited in high-dimensional settings. For this purpose, we study two promising distances: a Manhattan-type distance and a distance based on an orthogonal projection of the embedded points in the direction of the group centroids. We show that the NPMANOVA method and the KMANOVA method with the induced distance are essentially equivalent. We also show that the KMANOVA method with the other two distances performs considerably better than the NPMANOVA method. We illustrate the advantages of our approach in the context of genetic association studies and demonstrate its usefulness on Alzheimer’s disease data. We also provide a software implementation of the method that is available on GitHub https://github.com/8699vicente/Kmanova.

Due to the presence of multiple types of adverse events (AEs) with different levels of severity, the analysis of longitudinal toxicity data is a difficult task in cancer research. The current literature primarily relies on descriptive-based methods and lacks models that can effectively quantify the overall toxic burden experienced by patients over treatment without losing details of the impact of each AE. In this work, a novel taxonomy based on latent Markov models and compositional data techniques is proposed to model the Latent Overall Toxicity (LOTox) condition of each patient over cycles of treatment. Starting from observed categories of severity of multiple toxicities, the goal is to delineate distinct LOTox conditions and retrieve patients’ probabilities of being in a specific condition at a given cycle, as well as their risk of experiencing “worse" overall toxicity statuses compared to a reference “good" toxic condition. The proposed approach is applied to longitudinal toxicity data from the MRC BO06/EORTC 80931 randomized controlled trial for patients with osteosarcoma. The population of interest includes 377 patients who had successfully completed the six-cycle treatment. Personal characteristics and observed information on six toxicities are used to infer the unobserved LOTox status over the six cycles of chemotherapy. Provided that longitudinal toxicity data are available, the developed procedure is a flexible approach that can be adapted and applied to other cancer studies.

Style analysis is an asset class factor model aiming at obtaining information on the internal allocation of a financial portfolio and at comparing portfolios with similar investment strategies. The aim of the paper is to investigate the use of quantile regression to draw inferences on style coefficients. In particular, we compare an approximation widely used from practitioners, the Lobosco–Di Bartolomeo solution, with robust estimators based on constrained median regression. The inference process exploits a rolling window procedure based on subsampling theory. Different sets of outliers have been simulated in order to show differences in the efficiency, in the coverage error and in the length of the resulting confidence intervals. The proposed solution shows better performance in presence of outliers in Y, in X, or in X and Y, in terms both of empirical coverage and of interval lengths, i.e. whereas the performance of the classical solution deteriorates.

The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a given hypothesis with respect to the available information (prior law and data). To summarise this information, the posterior median is employed, allowing a simple assessment of the discrepancy with a fixed hypothesis. The Bayesian Discrepancy Measure assesses the compatibility of a single hypothesis with the observed data, as opposed to the more common comparative approach where a hypothesis is rejected in favour of a competing hypothesis. The proposed measure of evidence has properties of consistency and invariance. After presenting the definition of the measure for a parameter of interest, both in the absence and in the presence of nuisance parameters, we illustrate some examples showing its conceptual and interpretative simplicity. Finally, we compare a test procedure based on the Bayesian Discrepancy Measure, with the Full Bayesian Significance Test, a well-known Bayesian testing procedure for sharp hypotheses.

This paper introduces the pseudo-calibration estimators, a novel method that integrates a non-probability sample of big size with a probability sample, assuming both samples contain relevant information for estimating the population parameter. The proposed estimators share a structural similarity with the adjusted projection estimators and the difference estimators but they adopt a different inferential approach and informative setup. The pseudo-calibration estimators can be employed when the target variable is observed in the probability sample and, in the non-probability sample, it is observed correctly, observed with error, or predicted. This paper also introduces an original application of the jackknife-type method for variance estimation. A simulation study shows that the proposed estimators are robust and efficient compared to the regression data integration estimators that use the same informative setup. Finally, a further evaluation using real data is carried out.

[This corrects the article DOI: 10.1007/s10260-023-00690-5.].

The complexity of survey data and the availability of data from auxiliary sources motivate researchers to explore estimation methods that extend beyond traditional survey-based estimation. The U.S. Centers for Disease Control and Prevention's Behavioral Risk Factor Surveillance System (BRFSS) collects a wide range of health information, including whether respondents have a personal doctor. While the BRFSS focuses on state-level estimation, there is demand for county-level estimation of health indicators using BRFSS data. A hierarchical Bayes small area estimation model is developed to combine county-level BRFSS survey data with county-level data from auxiliary sources, while accounting for various sources of error and nested geographical levels. To mitigate extreme proportions and unstable survey variances, a transformation is applied to the survey data. Model-based county-level predictions are constructed for prevalence of having a personal doctor for all the counties in the U.S., including those where BRFSS survey data were not available. An evaluation study using only the counties with large BRFSS sample sizes to fit the model versus using all the counties with BRFSS data to fit the model is also presented.

The first cluster of coronavirus cases in Europe was officially detected on 21st February 2020 in Northern Italy, even if recent evidence showed sporadic first cases in Europe since the end of 2019. In this study, we have tested the presence of coronavirus in Italy and, even more importantly, we have assessed whether the virus had already spread sooner than 21st February. We use a counterfactual approach and certified daily data on the number of deaths (deaths from any cause, not only related to coronavirus) at the municipality level. Our estimates confirm that coronavirus began spreading in Northern Italy in mid-January.