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- Compositional risk capital allocations
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Abstract: 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.
PubDate: 2025-04-14
- A comparison of bandwidth selectors for moderate degree local polynomial
regression-
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Abstract: This paper presents a direct-plug-in bandwidth selector for local quadratic regression and local cubic regression, leveraging existing theoretical frameworks. Through extensive simulation studies, the performance of the proposed selector is evaluated using the Mean Squared Error (MSE) and Mean Absolute Error (MAE) criteria, in comparison with established methods. Additionally, empirical coverage of confidence intervals is analyzed to further assess its effectiveness. Practical applications of the methods are illustrated using wildfire rate of spread data.
PubDate: 2025-04-02
- Robustification of structural equation modelling via global sensitivity
analysis-
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Abstract: We propose a method for enhancing the robustness of Structural Equation Modelling (SEM), a multivariate statistical analysis technique employed for analyzing causal relationships among different aspects of given phenomena. This enhancement is achieved through the integration of Global Sensitivity Analysis, which assesses how uncertainties in model output can be attributed to various sources of input uncertainty. The robustification process involves several key steps, including bootstrapping evidence, error propagation, and uncertainty quantification. This method extends the approach named in the literature “modeling of the modelling process”. To illustrate this approach, we apply it to two previously published test cases where SEM is used. The first one is related to the impact of artificial intelligence adoption on employee engagement and the second one investigates the effects of service quality and environmental practices on the competitiveness and financial performance of hotels. By quantifying the uncertainty inherent in the inference of our test cases, this procedure increases the robustness of the results derived from the test cases, thus generating a more defensible inference.
PubDate: 2025-03-11
- Improved joint modeling of longitudinal and survival data using a poisson
regression approach-
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Abstract: Data of repeated measurements (longitudinal) and time-to-events (survival) are commonly recorded in studies. The joint model (JM) of longitudinal and survival data, which allows simultaneously analysis of the two types of outcomes, has been extensively discussed recently. JMs are computationally intensive due to large number of parameters and the complexity of fitting the survival submodel. The centerpiece of the survival submodel is the piecewise constant proportional hazard (PCPH). An alternative to PCPH for analysing survival data is the auxiliary Poisson regression model. However, the use of this approach in JMs has not been discussed. In this study, we propose using the auxiliary Poisson model as the survival part in a JM within a Bayesian framework. We conducted comprehensive simulation studies to assess the performance of our proposed method under various conditions and compared it to a published R package for JMs called JMbayes. Additionally, we used data from the Manitoba Follow-Up Study to illustrate the advantages and feasibility of our proposed method. The findings have showed that using the auxiliary Poisson approach as the survival submodel is a very promising method for jointly modeling longitudinal and survival data, as it helps decrease the computing burden.
PubDate: 2025-03-04
- Confidence intervals for Newton–Cotes quadratures based on
stationary point processes-
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Abstract: Motivated by the stereological application of volume estimation, this paper is concerned with numerical integration on the real line, employing function values at a finite set of randomly chosen points. The sampling points are modeled by a stationary point process, with the estimators being Newton–Cotes quadratures. Our comprehensive probabilistic analysis crucially extends existing results regarding the approximation error and variance, accommodating more general integrands and non-ergodic sampling processes. Notably, these findings are used to formulate novel asymptotic confidence intervals, a considerable challenge given the usual absence of limit distributions. To underscore the practicality of our approach, we apply it to a stereological simulation study. Specifically, we establish confidence intervals for the volume of a three-dimensional ellipsoid, based on section areas obtained from randomly positioned parallel planes.
PubDate: 2025-02-27
- Accelerated failure time and additive hazard models for combined
right-censored and left-truncated right-censored failure time data-
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Abstract: The semiparametric accelerated failure time and additive hazards models are commonly used alternatives to the proportional hazards model. For independent samples of right-censored or left-truncated right-censored failure time data, estimating equation based procedures are used to derive estimators for the unknown model parameters. In various applications, a sample data set can consist of multiple types of partially observed failure time data through the use of multiple sampling schemes or combination of multiple data sets. We propose three different estimation methodologies for estimating the unknown regression parameters in the accelerated failure time and additive hazards models using combined right-censored and left-truncated right-censored failure time data. These three methods are based on averaging the parametric estimators of the two samples, determining the zero-crossing of the summation of the two samples’ estimating equations and determining the zero-crossing of a single estimating equation based on the combination of the two samples. We assess the performance of the estimators through extensive simulation studies and use the estimators to model the factors affecting African lion mortality.
PubDate: 2025-02-25
- Addressing topic modelling via reduced latent space clustering
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Abstract: In the social sciences, topic modelling is gaining increased attention for its ability to automatically uncover the underlying themes within large corpora of textual data. This process typically involves two key phases: (i) identifying the words associated with language concepts, and (ii) clustering documents that share similar word distributions. In this study, motivated by the growing interest in automatic categorisation of policy documents and regulations, we leverage recent advancements in Bayesian factor models to develop a novel topic modelling approach. This enable us to represent the high-dimensional space defined by all possible observed words through a small set of latent variables, and simultaneously cluster the documents based on their distributions over these latent constructs. Here, groups and underlying constructs are interpreted as document topics and language concepts, respectively, with the number of dimensions not required in advance. Additionally, we demonstrate the effectiveness of our approach using synthetic data, providing a comparison with existing methods in the literature. The illustration of our approach on a corpus of Italian health public plans unveils intriguing patterns concerning the semantic structures used in ageing policies and document topic similarities.
PubDate: 2025-02-13
- The NBD-Dirichlet model for Italian sparkling wines: understanding
competitive relationships among brands-
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Abstract: The NBD-Dirichlet model is applied to describe the Italian market of sparkling wines by means of repeated purchases recorded by a sample of families over two years. Sparkling wine is a convenience good with a moderate level of involvement, high frequency of purchase and low perceived differentiation. The Italian market of sparkling wine is characterized by a large number of brands proposing similar products offered in supermarkets. This very large assortment represents a very particular situation, both in terms of sales strategies and consumer purchasing behavior. This specific type of market can be well represented by the NBD-Dirichlet model to obtain analyses that explain the competitive dynamics among brands and their relative performance. Results of model estimation identified at least three groups of brands with different positioning in the market. Managerial implications of these results are linked to the possibility for each single brand to compare actual performance with that estimated by the model and with competitors belonging to the same segment.
PubDate: 2025-01-27
- Enhancing business cycle analysis by integrating anomaly detection and
components decomposition of time series data-
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Abstract: This study presents an innovative approach for detecting and estimating outliers in time series data, emphasizing constrained-remaining components decomposition. The method extends the moving linear model to accommodate outliers, resulting in an enhanced moving linear model. A state-space representation improves computational efficiency through Bayesian estimation. We introduce a novel method for determining outlier positions, starting with initial estimates of the remaining components. The proposed methodology combines maximum likelihood and Bayesian-type estimation for effective outlier detection and estimation, guided by the minimum Akaike Information Criterion (AIC). Furthermore, we investigate outlier detection in time series data with seasonal components. Applications to real data, specifically the Index of Industrial Production (IIP) and Wholesale Commercial Sales (WCS) in Japan, showcase the simplicity and potential for automation in the proposed approach, making it a promising tool for time series analysis, particularly in constrained-remaining components decomposition.
PubDate: 2025-01-16
- Calibration and optimal transport approaches for harmonizing survey
weights-
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Abstract: Originally, the construction of weighting systems to estimate parameters of interest in survey data does not depend on the variables of interest. However, recent research raises questions about the practice of using specific weighting systems for each variable of interest, thus deviating from the universal nature of the weights proposed by survey data processing methods. This article examines the challenge of harmonizing weights for variables with different weighting systems in survey data processing, by presenting and comparing two methods: one that creates a common weight for both variables using the calibration method, and one that uses optimal transport to match the variables. A simulation study is carried out to evaluate the performance of these methods in different sampling scenarios and with continuous and categorical variables. The results of the simulation study show that the optimal transport method for weight harmonization can provide accurate parameter estimates in different scenarios, particularly in situations where disparities between sample and population distributions are large. It therefore appears to be a more versatile solution.
PubDate: 2025-01-16
- Hypothesis tests of indirect effects for multiple mediators
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Abstract: 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.
PubDate: 2025-01-16
- The use of multiple systems estimation to estimate the number of
unattributed paintings by Modigliani-
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Abstract: The number of unattributed paintings by Amedeo Modigliani is estimated, using the method of multiple systems estimation (MSE). Most major artists’ works are listed in one catalogue raisonné, but there are five catalogues purporting to list Modigliani paintings. These can be treated as list sources from which MSE can be applied. We obtain estimates by following the classical MSE approach using log-linear models, and compare these with estimates obtained via a Bayesian non-parametric latent class approach. We also consider the impact of fake paintings through sensitivity analyses. Our estimates point to there being around 20–120 unattributed Modigliani paintings.
PubDate: 2025-01-14
- Clustering of mortality paths with the Hellinger distance and
visualization through the DISTATIS technique-
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Abstract: Stochastic mortality models improve forecast accuracy through multipopulation approaches, yet lack rigorous criteria for country selection. This study introduces a novel, distance-based method using Hellinger distance and hierarchical clustering to identify countries with similar average mortality. Convergence or divergence of mortality paths is then checked visually by projecting the distances between countries in different years to a common Cartesian space using the DISTATIS technique. Analyzing mortality data from 1960 to 2019 for multiple countries from the Human Mortality Database via hierarchical clustering and DISTATIS visualization, I identify stable clusters and reveal convergence trends that are subsequently described through mortality indicators. The Hellinger distance outperforms other plausible choices of distances and the DISTATIS factors capture both the timing and dispersion of mortality. The findings offer a robust measure for country selection in multipopulation models, improving on the evaluation of convergence or divergence of mortality paths compared to methods based on life expectancy.
PubDate: 2025-01-07
- Monitoring road infrastructure from satellite images in Greater Maputo
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Abstract: The information about pavement surface type is rarely available in road network databases of developing countries although it represents a cornerstone of the design of efficient mobility systems. This research develops an automatic classification pipeline for road pavement which makes use of satellite images to recognize road segments as paved or unpaved. The proposed methodology is based on an object-oriented approach, so that each road is classified by looking at the distribution of its pixels in the RGB space. The proposed approach is proven to be accurate, inexpensive, and readily replicable in other cities.
PubDate: 2024-12-23
- A maximum statistic for the one-sided location-scale alternative in the
two-stage design-
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Abstract: An increase in location is typically accompanied by an increase in variability. Subsequently, the heteroscedasticity can indicate a treatment effect. Therefore, it may be appropriate to perform a location-scale test. A common statistic for a location-scale test is the sum of a location and scale statistic. As demonstrated by Neuhäuser (Biometri J 43:809–819, 2001), weighting the sum increases the power. Although weights cannot usually be reasonably selected a priori, a weighting is possible in an adaptive design using the information obtained in an interim analysis. Here, we propose an adaptive statistic that increases and stabilizes the power. The power performance in various situations for continuous and discrete distributions is investigated using Monte Carlo simulations, which reveal that the proposed statistic increases and stabilizes the power, thus rendering it a strong competitor to existing location-scale statistics. The new statistic is illustrated using real data.
PubDate: 2024-12-23
- An optimal exact interval for risk difference in 2$$\times$$2 contingency
tables with structural zeros-
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Abstract: In studies involving infectious diseases or two-step treatment research, the 2$$\times$$2 contingency table with a structural zero serves as a common framework for data collection. In biomedical studies and related fields, inferring the risk differences through confidence intervals is of significant importance. However, the reliability of approximate intervals based on asymptotic normality is questionable, particularly in small samples. This paper aims to address this limitation by proposing exact intervals for the risk difference, enhancing both reliability and precision. Initially, a novel interval is introduced using the restricted most probable method, which is then optimized via the h-function method to create an optimal exact interval. A comparative analysis is conducted, contrasting this proposed interval with others derived from methods such as the score method, inferential model method, and modified inferential model method. Numerical studies demonstrate the superiority of the proposed interval in terms of both infimum coverage probability and total interval length. Additionally, two illustrative examples are provided to demonstrate the practical application of this interval in real-world scenarios.
PubDate: 2024-12-09
- A finite mixture approach for the analysis of digital skills in Bulgaria,
Finland and Italy: the role of socio-economic factors-
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Abstract: The digital divide is the gap among population sub-groups in accessing and/or using digital technologies. Typically, older people show a lower propensity to have a broadband connection, use the Internet, and adopt new technologies than the younger ones. Motivated by the analysis of the heterogeneity in the use of digital technologies, we build a bipartite network concerning the presence of various digital skills in individuals from three different European countries: Bulgaria, Finland, and Italy. Bipartite networks provide a useful structure for representing relationships between two disjoint sets of nodes, formally called sending and receiving nodes. The goal is to perform a clustering of individuals (sending nodes) from each country based on their digital skills (receiving nodes). In this regard, we employ a Mixture of Latent Trait Analyzers (MLTA) with concomitant variables, which allows us to (i) cluster individuals according to their profile; (ii) analyze how socio-economic and demographic characteristics, as well as intergenerational ties, influence individual digitalization. Results show that the type of digitalization substantially depends on age, income and level of education, while the presence of children in the household seems to play an important role in the digitalization process in Italy and Finland only.
PubDate: 2024-11-25
- Group penalized expectile regression
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Abstract: The asymmetric least squares regression (or expectile regression) allows estimating unknown expectiles of the conditional distribution of a response variable as a function of a set of predictors and can handle heteroscedasticity issues. High dimensional data, such as omics data, are error prone and usually display heterogeneity. Such heterogeneity is often of scientific interest. In this work, we propose the Group Penalized Expectile Regression (GPER) approach, under high dimensional settings. GPER considers implementation of sparse expectile regression with group Lasso penalty and the group non-convex penalties. However, GPER may fail to tell which groups variables are important for the conditional mean and which groups of variables are important for the conditional scale/variance. To that end, we further propose a COupled Group Penalized Expectile Regression (COGPER) regression which can be efficiently solved by an algorithm similar to that for solving GPER. We establish theoretical properties of the proposed approaches. In particular, GPER and COGPER using the SCAD penalty or MCP is shown to consistently identify the two important subsets for the mean and scale simultaneously. We demonstrate the empirical performance of GPER and COGPER by simulated and real data.
PubDate: 2024-11-20
- A Kernel approach for extending nonparametric multivariate analysis of
variance in high-dimensional settings-
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Abstract: 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.
PubDate: 2024-11-18
- Longitudinal latent overall toxicity (LOTox) profiles in osteosarcoma: a
new taxonomy based on latent Markov models-
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Abstract: 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.
PubDate: 2024-10-29
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