Search Results (29)

The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian discrepancy measure used in testing precise statistical hypotheses. In particular, we derive results on third-order asymptotic approximations and skewed approximations for univariate posterior distributions, including cases with nuisance parameters, demonstrating improved accuracy in capturing posterior shape with little additional computational cost over simple first-order approximations. For third-order approximations, connections to frequentist inference via matching priors are highlighted. Moreover, the definition of the Bayesian discrepancy measure and the proposed methodology are extended to the multivariate setting, employing tractable skew-normal posterior approximations obtained via derivative matching at the mode. Accurate multivariate approximations for the Bayesian discrepancy measure are then derived by defining credible regions based on an optimal transport map that transforms the skew-normal approximation to a standard multivariate normal distribution. The performance and practical benefits of these higher-order and skewed approximations are illustrated through two examples. Full article

We combine two well-known statements of results in the statistical and mathematical literature, one related to symmetric continuous distributions and the other to the integration of functions, to obtain some new results regarding symmetric distributions and involving the value at risk and the tail value at risk, well-known tools used in actuarial and financial statistics, among others. Generalizations of the skew normal distribution in its univariate and multivariate versions obtained from one of the results are also shown, and a new method is proposed for generating families of skewed continuous distributions. Full article

Background: The effectiveness of the immunity provided by SARS-CoV-2 vaccines is an important public health issue. We analyzed the determinants of 12-month serology in a multicenter European cohort of vaccinated healthcare workers (HCW). Methods: We analyzed the sociodemographic characteristics and levels of anti-SARS-CoV-2 spike antibodies (IgG) in a cohort of 16,101 vaccinated HCW from eleven centers in Germany, Italy, Romania, Slovakia and Spain. Considering the skewness of the distribution, the serological levels were transformed using log or cubic standardization and normalized by dividing them by center-specific standard errors. We fitted center-specific multivariate regression models to estimate the cohort-specific relative risks (RR) of an increase of one standard deviation of log or cubic antibody level and the corresponding 95% confidence interval (CI) for different factors and combined them in random-effects meta-analyses. Results: We included 16,101 HCW in the analysis. A high antibody level was positively associated with age (RR = 1.04, 95% CI = 1.00–1.08 per 10-year increase), previous infection (RR = 1.78, 95% CI 1.29–2.45) and use of Spikevax [Moderna] with combinations compared to Comirnaty [BioNTech/Pfizer] (RR = 1.07, 95% CI 0.97–1.19) and was negatively associated with the time since last vaccine (RR = 0.94, 95% CI 0.91–0.98 per 30-day increase). Conclusions: These results provide insight about vaccine-induced immunity to SARS-CoV-2, an analysis of its determinants and quantification of the antibody decay trend with time since vaccination. Full article

In this article, we derive a closed-form expression for computing the probabilities of p-dimensional rectangles by means of a multivariate skew-normal distribution. We use a stochastic representation of the multivariate skew-normal/independent distributions to derive expressions that relate their probability density functions to the expected values of positive random variables. We also obtain an analogous expression for probabilities of p-dimensional rectangles for these distributions. Based on this, we propose a procedure based on Monte Carlo integration to evaluate the probabilities of p-dimensional rectangles through multivariate skew-normal/independent distributions. We use these findings to evaluate the probability density functions of a truncated version of this class of distributions, for which we also suggest a scheme to generate random vectors by using a stochastic representation involving a truncated multivariate skew-normal random vector. Finally, we derive distributional properties involving affine transformations and marginalization. We illustrate graphically several of our methodologies and results derived in this article. Full article

We introduce a quantile-based multivariate log-normal distribution, providing a new multivariate skewed distribution with positive support. The parameters of this distribution are interpretable in terms of quantiles of marginal distributions and associations between pairs of variables, a desirable feature for statistical modeling purposes. We derive statistical properties of the quantile-based multivariate log-normal distribution involving the transformations, closed-form expressions for the mixed moments, expected value, covariance matrix, mode, Shannon entropy, and Kullback–Leibler divergence. We also present results on marginalization, conditioning, and independence. Additionally, we discuss parameter estimation and verify its performance through simulation studies. We evaluate the model fitting based on Mahalanobis-type distances. An application to children data is presented. Full article

With the development and proliferation of unmanned weapons systems, path planning is becoming increasingly important. Existing path-planning algorithms mainly assume a well-known environment, and thus pre-planning is desirable, but the actual ground battlefield is uncertain, and numerous contingencies occur. In this study, we present a novel, efficient path-planning algorithm based on a potential field that quickly changes the path in a constantly changing environment. The potential field is composed of a set of functions representing enemy threats and a penalty term representing distance to the target area. We also introduce a new threat function using a multivariate skew-normal distribution that accurately expresses the enemy threat in ground combat. Full article

Background: The persistence of antibody levels after COVID-19 vaccination has public health relevance. We analyzed the determinants of quantitative serology at 9 months after vaccination in a multicenter cohort. Methods: We analyzed data on anti-SARS-CoV-2 spike antibody levels at 9 months from the first dose of vaccinated HCW from eight centers in Italy, Germany, Spain, Romania and Slovakia. Serological levels were log-transformed to account for the skewness of the distribution and normalized by dividing them by center-specific standard errors. We fitted center-specific multivariate regression models to estimate the cohort-specific relative risks (RR) of an increase of one standard deviation of log antibody level and the corresponding 95% confidence interval (CI), and combined them in random-effects meta-analyses. Finally, we conducted a trend analysis of 1 to 7 months’ serology within one cohort. Results: We included 20,216 HCW with up to two vaccine doses and showed that high antibody levels were associated with female sex (p = 0.01), age (RR = 0.87, 95% CI = 0.86–0.88 per 10-year increase), 10-day increase in time since last vaccine (RR = 0.97, 95% CI 0.97–0.98), previous infection (3.03, 95% CI = 2.92–3.13), two vaccine doses (RR = 1.22, 95% CI = 1.09–1.36), use of Spikevax (OR = 1.51, 95% CI = 1.39–1.64), Vaxzevria (OR = 0.57, 95% CI = 0.44–0.73) or heterologous vaccination (OR = 1.33, 95% CI = 1.12–1.57), compared to Comirnaty. The trend in the Bologna cohort, based on 3979 measurements, showed a decrease in mean standardized antibody level from 8.17 to 7.06 (1–7 months, p for trend 0.005). Conclusions: Our findings corroborate current knowledge on the determinants of COVID-19 vaccine-induced immunity and declining trend with time. Full article

The multivariate skew-t distribution plays an important role in statistics since it combines skewness with heavy tails, a very common feature in real-world data. A generalization of this distribution is the truncated multivariate skew-t distribution which contains the truncated multivariate t distribution and the truncated multivariate skew-normal distribution as special cases. In this article, we study several distributional properties of the truncated multivariate skew-t distribution involving affine transformations, marginalization, and conditioning. The generation of random samples from this distribution is described. Full article

The multivariate skew-normal distribution is useful for modeling departures from normality in data through parameters controlling skewness. Recently, several extensions of this distribution have been proposed in the statistical literature, among which the truncated multivariate skew-normal distribution is the foremost. Truncated distributions appear frequently in various theoretical and applied statistical problems. In this article, we study several properties of the truncated multivariate skew-normal distribution. We obtain distributional results through affine transformations, marginalization, and conditioning. Furthermore, the log-concavity of the joint probability density function is established. Full article

This paper is concerned with the multivariate extended skew-normal [MESN] and multivariate extended skew-Student [MEST] distributions, that is, distributions in which the location parameters of the underlying truncated distributions are not zero. The extra parameter leads to greater variability in the moments and critical values, thus providing greater flexibility for empirical work. It is reported in this paper that various theoretical properties of the extended distributions, notably the limiting forms as the magnitude of the extension parameter, denoted $\tau$ in this paper, increases without limit. In particular, it is shown that as $\tau$, the limiting forms of the MESN and MEST distributions are different. The effect of the difference is exemplified by a study of stockmarket crashes. A second example is a short study of the extent to which the extended skew-normal distribution can be approximated by the skew-Student. Full article

This review is about verifying and generalizing the supremum test statistic developed by Balakrishnan et al. Exhaustive simulation studies are conducted for various dimensions to determine the effect, in terms of empirical size, of the supremum test statistic developed by Balakrishnan et al. to test multivariate skew-normality. Monte Carlo simulation studies indicate that the Type-I error of the supremum test can be controlled reasonably well for various dimensions for given nominal significance levels 0.05 and 0.01. Cut-off values are provided for the number of samples required to attain the nominal significance levels 0.05 and 0.01. Some new and relevant information of the supremum test statistic are reported here. Full article

Multivariate skew-symmetric-normal (MSSN) distributions have been recognized as an appealing tool for modeling data with non-normal features such as asymmetry and heavy tails, rendering them suitable for applications in diverse areas. We introduce a richer class of MSSN distributions based on a scale-shape mixture of (multivariate) flexible skew-symmetric normal distributions, called the SSMFSSN distributions. This very general class of SSMFSSN distributions can capture various shapes of multimodality, skewness, and leptokurtic behavior in the data. We investigate some of its probabilistic characterizations and distributional properties which are useful for further methodological developments. An efficient EM-type algorithm designed under the selection mechanism is advocated to compute the maximum likelihood (ML) estimates of parameters. Simulation studies as well as applications to a real dataset are employed to illustrate the usefulness of the presented methods. Numerical results show the superiority of our proposed model in comparison to several existing competitors. Full article

This paper addresses the projection pursuit problem assuming that the distribution of the input vector belongs to the flexible and wide family of multivariate scale mixtures of skew normal distributions. Under this assumption, skewness-based projection pursuit is set out as an eigenvector problem, described in terms of the third order cumulant matrix, as well as an eigenvector problem that involves the simultaneous diagonalization of the scatter matrices of the model. Both approaches lead to dominant eigenvectors proportional to the shape parametric vector, which accounts for the multivariate asymmetry of the model; they also shed light on the parametric interpretability of the invariant coordinate selection method and point out some alternatives for estimating the projection pursuit direction. The theoretical findings are further investigated through a simulation study whose results provide insights about the usefulness of skewness model-based projection pursuit in the statistical practice. Full article

Symmetric elliptical distributions have been intensively used in data modeling and robustness studies. The area of applications was considerably widened after transforming elliptical distributions into the skew elliptical ones that preserve several good properties of the corresponding symmetric distributions and increase possibilities of data modeling. We consider three-parameter p-variate skew t-distribution where p-vector $\mathbf{\mu }$ is the location parameter, $\mathsf{\Sigma }:p\times p$ is the positive definite scale parameter, p-vector $\mathbf{\alpha }$ is the skewness or shape parameter, and the number of degrees of freedom $\nu$ is fixed. Special attention is paid to the two-parameter distribution when $\mathbf{\mu }=\mathbf{0}$ that is useful for construction of the skew t-copula. Expressions of the parameters are presented through the moments and parameter estimates are found by the method of moments. Asymptotic normality is established for the estimators of $\mathsf{\Sigma }$ and $\mathbf{\alpha }$. Convergence to the asymptotic distributions is examined in simulation experiments. Full article

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples. Full article