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A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough simulation study is conducted to investigate: the efficiency with Normal and heavy-tailed errors, the robustness under contamination, the computational time, the affine equivariance and breakdown value of the regression estimator. Two classical data-sets often used in the literature and a real socioeconomic data-set about the Living Environment Deprivation of areas in Liverpool (UK), are studied. The results from the simulations and the real data examples show the advantages of the proposed robust estimator in regression. [ABSTRACT FROM AUTHOR]

In this paper we examine in detail some of the modeling capabilities of the stationary m -state BMAP , with simultaneous events up to size k , noted BMAP m ( k ) . Specifically, we study the forms of the auto-correlation functions of the inter-event times and event sizes. We provide a novel characterization of the functions which is suitable for analyzing the dependence patterns. In particular, this allows one to prove a geometrically decrease to zero of the functions and to identify four correlation patterns, when m =2 . The case m ≥ 3 is illustrated via an extensive simulation study, from which it can be deduced that, as expected, richer structures can be obtained as m increases. In addition, the influence of the dependence patterns for both auto-correlation functions for the BMAP 2 ( 2 ) in the counting process has been explored through an empirical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some stochastic comparisons in terms of likelihood ratio ordering between spacings from independent random variables exponentially distributed with different scale parameters. We partially solve some open problems in [Wen S, Lu Q, Hu T. Likelihood ratio orderings of spacings of heterogeneous exponential random variables. J Multivariate Anal. 2007;98:743–756] for a one-sample problem and in [Hu T, Lu Q, Wen S. Stochastic comparisons and dependence of spacings from two samples of exponential random variables. Commun Stat – Theory Methods 2006;35:979–988] for a two-sample problem. Specifically, we prove that the second spacing is always smaller than the third spacing in terms of the likelihood ratio order and we provide the ordering among all spacings in the casen=4. In the two-sample case, we establish comparisons between the second spacings related to each sample under certain conditions. [ABSTRACT FROM AUTHOR]

In this paper, comparisons of allocation policies of components in two-parallel-series systems with two types of components are provided with respect to both hazard rate and reversed hazard rate orders. The main results indicate that the lifetime of these kinds of system is stochastically maximized by unbalancing the two classes of components as much as possible. We only assume that the two distributions implied in the model have proportional hazard rates. The same type of comparisons are also given for the dual model, the two-series-parallel systems, but assuming that the distributions implied in the model have proportional reversed hazard rates, and therefore the final conclusion is the opposite; that is, the reliability of the system improves as the similarity between the two parallel subsystems increases. [ABSTRACT FROM PUBLISHER]

Abstract: In this article we obtain some new results in the area of stochastic comparisons of simple and normalized spacings from two samples of heterogeneous exponential random variables. Specifically, we investigate conditions under which successive spacings are ordered in the likelihood ratio ordering. We also show some applications of our results to the multiple-outlier case. [Copyright &y& Elsevier]

Abstract: Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied and also an application in reliability theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t 0 aging notion. [Copyright &y& Elsevier]

Abstract: In this article, we partially solve a conjecture by Kochar and Korwar (1996) in relation to the normalized spacings of the order statistics of a sample of independent exponential random variables with different scale parameters. In the case of a sample of size , they proved the ordering of the normalized spacings and conjectured that result holds for all . We prove this conjecture for for both spacings and normalized spacings and generalize some results to . [Copyright &y& Elsevier]

A novel discriminant analysis (DA) method is proposed, based on the robust reweighted shrinkage estimators and a robust Mahalanobis distance with an adjusted quantile as threshold. A simulation study is done to evaluate the performance of the proposed approach in comparison with the classical DA and the other robust alternatives from the literature. The approach is also illustrated using real dataset examples: a geochemical and environmental dataset known as the Kola Project and a second data containing the spectra of different cultivars of a fruit. The results show the appropriateness of the method while being computationally efficient at the same time. Additional simulations are included to show the additional benefits in outlier detection. • The classical discriminant analysis rule is highly influenced by outliers. • The robust alternatives worsens its performance in high dimension. • The proposed RADAS approach have good performance while being computationally efficient. • The method shows advantages with real examples like the geochemical and environmental dataset known as the Kola Project. • There are additional benefits in outlier detection. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of designing a queueing system. Given arrival and service data, our objective is to choose the optimal number of servers so as to minimize an expected cost function which depends on quantities, such as the number of customers in the queue. A semiparametric approach based on Erlang mixture distributions is used to model the general interarrival time distribution. Given the sample data, Bayesian Markov Chain Monte Carlo methods are used to estimate the system parameters and the predictive distributions of the usual performance measures. We can then use these estimates to minimize the steady-state expected total cost rate as a function of the control parameter c. We provide a numerical example based on real data obtained from a bank in Madrid. [Copyright &y& Elsevier]

The purpose of this paper is to derive bounds on the marginal distributions of a discrete-time claim process S with correlated claims. These bounds are based on stochastic comparison in convex order and in Laplace transform order of the process S with two corresponding processes S and S having, respectively, uncorrelated and weakly correlated claims. The relevance of these comparisons is due to the simple structure of the processes S and S, which are nothing else than a random walk and a mixed random walk. The paper also contains the proof of the closure under mixture property of some dependence orders, like supermodular and PQD, and some applications of the main results. [ABSTRACT FROM AUTHOR]

Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent and non-exponential inter-failure times (in contexts as queuing, risk or reliability, among others). The novel two-dimensional MMPP allows for dependence between the two sequences of inter-failure times, while at the same time preserves the MMPP properties, marginally. The generalization is based on the Marshall–Olkin exponential distribution. Inference is undertaken for the new model through a method combining a matching moments approach with an Approximate Bayesian Computation (ABC) algorithm. The performance of the method is shown on simulated and real datasets representing times and distances covered between consecutive failures in a public transport company. For the real dataset, some quantities of importance associated with the reliability of the system are estimated as the probabilities and expected number of failures at different times and distances covered by trains until the occurrence of a failure. • A bivariate Markov modulated Poisson process is introduced. • A matrix formulation of the model is proposed that allows attacking the reliability of the process in a feasible way. • A sequential fitting approach via a moments matching combined with an ABC algorithm is provided. • The suitability of the results is illustrated through the analysis of a real dataset from the reliability context. [ABSTRACT FROM AUTHOR]

AbstractThe Network Scale-up Methods (NSUM) are methods to estimate unknown populations based on indirect surveys in which the participants provide information about aggregated data of their acquaintances. This preserves the privacy and may lead to higher participation. During the last thirty years, new NSUM estimators have emerged. However, conditions related to the design of the experiments and the robustness of the estimators have not been studied in depth, especially in a realistic simulation environment. This study aims to compare nine NSUM estimators under relevant conditions in the literature through simulation experiments. We have analyzed how the NSUM is affected by the network topology, transmission and recall errors, the distribution of the unknown subpopulation, the number and sizes of subpopulations, and sample size. This article shows that some NSUM estimators barely used are better and more robust to some conditions, especially when the network is scale-free or under barrier effects. In addition, some methods are very sensitive to recall errors. In terms of the subpopulations configuration, we observe that the number of known subpopulations usually employed is quite large and that the most common NSUM is robust to the number and sizes of the subpopulations. [ABSTRACT FROM AUTHOR]

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing interest in the overlapping area between neural networks and more traditional statistical methods, which can help overcome those problems. In this article, a mathematical framework relating neural networks and polynomial regression is explored by building an explicit expression for the coefficients of a polynomial regression from the weights of a given neural network, using a Taylor expansion approach. This is achieved for single hidden layer neural networks in regression problems. The validity of the proposed method depends on different factors like the distribution of the synaptic potentials or the chosen activation function. The performance of this method is empirically tested via simulation of synthetic data generated from polynomials to train neural networks with different structures and hyperparameters, showing that almost identical predictions can be obtained when certain conditions are met. Lastly, when learning from polynomial generated data, the proposed method produces polynomials that approximate correctly the data locally. [ABSTRACT FROM AUTHOR]

In high-dimensional supervised learning problems, sparsity constraints in the solution often lead to better performance and interpretability of the results. For problems in which covariates are grouped and sparse structure are desired, both on group and within group levels, the sparse-group lasso (SGL) regularization method has proved to be very efficient. Under its simplest formulation, the solution provided by this method depends on two weight parameters that control the penalization on the coefficients. Selecting these weight parameters represents a major challenge. In most of the applications of the SGL, this problem is left aside, and the parameters are either fixed based on a prior information about the data, or chosen to minimize some error function in a grid of possible values. However, an appropriate choice of the parameters deserves more attention, considering that it plays a key role in the structure and interpretation of the solution. In this sense, we present a gradient-free coordinate descent algorithm that automatically selects the regularization parameters of the SGL. We focus on a more general formulation of this problem, which also includes individual penalizations for each group. The advantages of our approach are illustrated using both real and synthetic datasets. for this article are available online. [ABSTRACT FROM AUTHOR]

We present definitions and properties of the fast massive unsupervised outlier detection (FastMUOD) indices, used for outlier detection (OD) in functional data. FastMUOD detects outliers by computing, for each curve, an amplitude, magnitude, and shape index meant to target the corresponding types of outliers. Some methods adapting FastMUOD to outlier detection in multivariate functional data are then proposed. These include applying FastMUOD on the components of the multivariate data and using random projections. Moreover, these techniques are tested on various simulated and real multivariate functional datasets. Compared with the state of the art in multivariate functional OD, the use of random projections showed the most effective results with similar, and in some cases improved, OD performance. Based on the proportion of random projections that flag each multivariate function as an outlier, we propose a new graphical tool, the magnitude‐shape‐amplitude (MSA) plot, useful for visualizing the magnitude, shape and amplitude outlyingness of multivariate functional data. [ABSTRACT FROM AUTHOR]

Symptoms-based detection of SARS-CoV-2 infection is not a substitute for precise diagnostic tests but can provide insight into the likely level of infection in a given population. This study uses symptoms data collected in the Global COVID-19 Trends and Impact Surveys (UMD Global CTIS), and data on variants sequencing from GISAID. This work, conducted in January of 2022 during the emergence of the Omicron variant (subvariant BA.1), aims to improve the quality of infection detection from the available symptoms and to use the resulting estimates of infection levels to assess the changes in vaccine efficacy during a change of dominant variant; from the Delta dominant to the Omicron dominant period. Our approach produced a new symptoms-based classifier, Random Forest, that was compared to a ground-truth subset of cases with known diagnostic test status. This classifier was compared with other competing classifiers and shown to exhibit an increased performance with respect to the ground-truth data. Using the Random Forest classifier, and knowing the vaccination status of the subjects, we then proceeded to analyse the evolution of vaccine efficacy towards infection during different periods, geographies and dominant variants. In South Africa, where the first significant wave of Omicron occurred, a significant reduction of vaccine efficacy is observed from August-September 2021 to December 2021. For instance, the efficacy drops from 0.81 to 0.30 for those vaccinated with 2 doses (of Pfizer/BioNTech), and from 0.51 to 0.09 for those vaccinated with one dose (of Pfizer/BioNTech or Johnson & Johnson). We also extended the study to other countries in which Omicron has been detected, comparing the situation in October 2021 (before Omicron) with that of December 2021. While the reduction measured is smaller than in South Africa, we still found, for instance, an average drop in vaccine efficacy from 0.53 to 0.45 among those vaccinated with two doses. Moreover, we found a significant negative (Pearson) correlation of around − 0.6 between the measured prevalence of Omicron in several countries and the vaccine efficacy in those same countries. This prediction, in January of 2022, of the decreased vaccine efficacy towards Omicron is in line with the subsequent increase of Omicron infections in the first half of 2022. [ABSTRACT FROM AUTHOR]

Symptoms-based detection of SARS-CoV-2 infection is not a substitute for precise diagnostic tests but can provide insight into the likely level of infection in a given population. This study uses symptoms data collected in the Global COVID-19 Trends and Impact Surveys (UMD Global CTIS), and data on variants sequencing from GISAID. This work, conducted in January of 2022 during the emergence of the Omicron variant (subvariant BA.1), aims to improve the quality of infection detection from the available symptoms and to use the resulting estimates of infection levels to assess the changes in vaccine efficacy during a change of dominant variant; from the Delta dominant to the Omicron dominant period. Our approach produced a new symptoms-based classifier, Random Forest, that was compared to a ground-truth subset of cases with known diagnostic test status. This classifier was compared with other competing classifiers and shown to exhibit an increased performance with respect to the ground-truth data. Using the Random Forest classifier, and knowing the vaccination status of the subjects, we then proceeded to analyse the evolution of vaccine efficacy towards infection during different periods, geographies and dominant variants. In South Africa, where the first significant wave of Omicron occurred, a significant reduction of vaccine efficacy is observed from August-September 2021 to December 2021. For instance, the efficacy drops from 0.81 to 0.30 for those vaccinated with 2 doses (of Pfizer/BioNTech), and from 0.51 to 0.09 for those vaccinated with one dose (of Pfizer/BioNTech or Johnson & Johnson). We also extended the study to other countries in which Omicron has been detected, comparing the situation in October 2021 (before Omicron) with that of December 2021. While the reduction measured is smaller than in South Africa, we still found, for instance, an average drop in vaccine efficacy from 0.53 to 0.45 among those vaccinated with two doses. Moreover, we found a significant negative (Pearson) correlation of around − 0.6 between the measured prevalence of Omicron in several countries and the vaccine efficacy in those same countries. This prediction, in January of 2022, of the decreased vaccine efficacy towards Omicron is in line with the subsequent increase of Omicron infections in the first half of 2022. [ABSTRACT FROM AUTHOR]

This article presents a new semidistance for functional observations that generalizes the Mahalanobis distance for multivariate datasets. The main characteristics of the functional Mahalanobis semidistance are shown. To illustrate the applicability of this measure of proximity between functional observations, new versions of several well-known functional classification procedures are developed using the functional Mahalanobis semidistance. A Monte Carlo study and the analysis of two real examples indicate that the classification methods used in conjunction with the functional Mahalanobis semidistance give better results than other well-known functional classification procedures. This article has supplementary material online. [ABSTRACT FROM PUBLISHER]

In this paper, we describe statistical inference and prediction for software reliability models in the presence of covariate information. Specifically, we develop a semiparametric, Bayesian model using Gaussian processes to estimate the numbers of software failures over various time periods when it is assumed that the software is changed after each time period and that software metrics information is available after each update. Model comparison is also carried out using the deviance information criterion, and predictive inferences on future failures are shown. Real-life examples are presented to illustrate the approach. [ABSTRACT FROM AUTHOR]

Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which are extremely sensitive to the presence of outliers or heavy tailed distributions. In contrast, quantile regression is an alternative to OLS that computes robust quantile based estimates. In this work, the multivariate PLS is extended to the quantile regression framework, obtaining a theoretical formulation of the problem and a robust dimensionality reduction technique that we call fast partial quantile regression (fPQR), that provides quantile based estimates. An efficient implementation of fPQR is also derived, and its performance is studied through simulation experiments and the chemometrics well known biscuit dough dataset, a real high dimensional example. • The fast partial quantile regression estimator extends PLS to quantile regression. • fPQR is a dimension reduction technique based on quantiles. • fPQR is computationally fast and straightforward. • fPQR is a robust estimator capable of dealing with heteroscedasticity and outliers. [ABSTRACT FROM AUTHOR]

• An aggregate loss model with dependent losses is considered. • The loss occurrence process is governed by a Markov renewal process. • A maximum likelihood approach is examined for inference for the loss occurrence process. • Novel descriptors to measure persistence in the loss occurrence process are obtained. • The approach is illustrated using a real OpRisk database. In this article we consider an aggregate loss model with dependent losses. The loss occurrence process is governed by a two-state Markovian arrival process (M A P 2), a Markov renewal process that allows for (1) correlated inter-loss times, (2) non-exponentially distributed inter-loss times and, (3) overdisperse loss counts. Some quantities of interest to measure persistence in the loss occurrence process are obtained. Given a real OpRisk database, the aggregate loss model is estimated by fitting separately the inter-loss times and severities. The M A P 2 is estimated via direct maximization of the likelihood function, and severities are modeled by the heavy-tailed, double-Pareto Lognormal distribution. In comparison with the fit provided by the Poisson process, the results point out that taking into account the dependence and overdispersion in the inter-loss times distribution leads to higher capital charges. [ABSTRACT FROM AUTHOR]

This paper introduces stringing via Manifold Learning (ML-stringing), an alternative to the original stringing based on Unidimensional Scaling (UDS). Our proposal is framed within a wider class of methods that map high-dimensional observations to the infinite space of functions, allowing the use of Functional Data Analysis (FDA). Stringing handles general high-dimensional data as scrambled realizations of an unknown stochastic process. Therefore, the essential feature of the method is a rearrangement of the observed values. Motivated by the linear nature of UDS and the increasing number of applications to biosciences (e.g., functional modeling of gene expression arrays and single nucleotide polymorphisms, or the classification of neuroimages) we aim to recover more complex relations between predictors through ML. In simulation studies, it is shown that ML-stringing achieves higher-quality orderings and that, in general, this leads to improvements in the functional representation and modeling of the data. The versatility of our method is also illustrated with an application to a colon cancer study that deals with high-dimensional gene expression arrays. This paper shows that ML-stringing is a feasible alternative to the UDS-based version. Also, it opens a window to new contributions to the field of FDA and the study of high-dimensional data. [ABSTRACT FROM AUTHOR]

In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional notions into the MEVT, giving the opportunity to characterize the recently introduced directional multivariate quantiles (DMQ) at high levels. Then, an out-sample estimation method for these quantiles is given. A bootstrap procedure carries out the estimation of the tuning parameter in this multivariate framework and helps with the estimation of the DMQ. Asymptotic normality for the proposed estimator is provided and the methodology is illustrated with simulated data-sets. Finally, a real-life application to a financial case is also performed. [ABSTRACT FROM AUTHOR]

Publisher Correction: Using survey data to estimate the impact of the omicron variant on vaccine efficacy against COVID-19 infection The original article can be found online at https://doi.org/10.1038/s41598-023-27951-3. Correction to: I Scientific Reports i https://doi.org/10.1038/s41598-023-27951-3, published online 17 January 2023 The original version of this Article contained a spelling error in the name of the author Nina Rescic, which was incorrectly given as Nina rescic. [Extracted from the article]

Gender violence is a problem that affects millions of people worldwide. Among its many manifestations Intimate Partner Violence (IPV) is one of the most common. In Spain, a police monitoring protocol has been developed to minimize recidivism in IPV cases. This protocol is complemented by VioGén, an Intimate Partner Violence Risk Assessment Tool (IPVRAT) created by the Spanish State Secretariat for Security of the Ministry of Interior (SES) for risk prediction. VioGén's goal is to help the authorities determine what security and safety measures are most suitable. This paper improves on the current version of VioGén by introducing a model based on machine learning and data science and by studying the predictive value of exogenous and historical variables. The model is fitted on an anonymized database provided by SES and extracted from VioGén. This database includes the 2-year evolution of 46,047 new cases of IPV violence reported between October 2016 and December 2017, making it the largest database analyzed in the field. Obtained results show a clear improvement in the predictive capabilities of the new model against the original system, where it would have corrected more than 25% of the infra-protected cases, while improving the overall accuracy at the same time. Finally, lessons learned from the performed study and experiments are reported to aid in the design of future IPVRAT. In particular, insights show that IPVRAT should not treat cases statically as the incorporation of information regarding their evolution improves significantly the model's performance. • Analysis of the largest dataset in IPVRAT to date: 2-year evolution of 46,047 cases. • Study of the predictive value of exogenous and historical variables. • New research paradigm: the direct estimation of the Optimal Protection Level. • Comparison of multiclass vs ordinal classification paradigms in the context of IPV. • New model that corrects over 25% of the cases infra-protected by the original system. [ABSTRACT FROM AUTHOR]

Over the last decade, regularized regression methods have offered alternatives for performing multi-marker analysis and feature selection in a whole genome context. The process of defining a list of genes that will characterize an expression profile remains unclear. It currently relies upon advanced statistics and can use an agnostic point of view or include some a priori knowledge, but overfitting remains a problem. This paper introduces a methodology to deal with the variable selection and model estimation problems in the high-dimensional set-up, which can be particularly useful in the whole genome context. Results are validated using simulated data and a real dataset from a triple-negative breast cancer study. [ABSTRACT FROM AUTHOR]