Sabrina Giordano

Sex and Age Specificity of Susceptibility Genes Modulating Survival at Old Age

Objective: We aimed to investigate the influence of the genetic variability of candidate genes on survival at old age in good health. Methods: First, on the basis of a synthetic survival curve constructed using historic mortality data taken from the Italian population from 1890 onward, we defined three age classes ranging from 18 to 106 years. Second, we assembled a multinomial logistic regression model to evaluate the effect of dichotomous variables (genotypes) on the probability to be assigned to a specific category (age class). Third, we applied the regression model to a cross-sectional dataset (10 genes; 972 subjects selected for healthy status) categorized according to age and sex. Results: We found that genetic factors influence survival at advanced age in good health in a sex- and age-specific way. Furthermore, we found that genetic variability plays a stronger role in males than in females and that, in both genders, its impact is especially important at very old ages. Conclusions: The analyses presented here underline the age-specific effect of the gene network in modulating survival at advanced age in good health.

Maximum likelihood estimation in Dagum distribution with censored samples

In this work, we show that the Dagum distribution [3] may be a competitive model for describing data which include censored observations in lifetime and reliability problems. Maximum likelihood estimates of the three parameters of the Dagum distribution are determined from samples with type I right and type II doubly censored data. We perform an empirical analysis using published censored data sets: in certain cases, the Dagum distribution fits the data better than other parametric distributions that are more commonly used in survival and reliability analysis. Graphical comparisons confirm that the Dagum model behaves better than a number of competitive distributions in describing the empirical hazard rate of the analyzed data. A probability plot to provide graphical check of the appropriateness of the Dagum model for right censored data is constructed, and the details are given in the appendix. Finally, a simulation study that shows the good performance of the maximum likelihood estimators of the Dagum shape parameters for finite type II doubly censored samples is carried out.

A stress–strength model with dependent variables to measure household financial fragility

The paper is inspired by the stress–strength models in the reliability literature, in which given the strength (Y) and the stress (X) of a component, its reliability is measured by P(X < Y). In this literature, X and Y are typically modeled as independent. Since in many applications such an assumption might not be realistic, we propose a copula approach in order to take into account the dependence between X and Y. We then apply a copula-based approach to the measurement of household financial fragility. Specifically, we define as financially fragile those households whose yearly consumption (X) is higher than income (Y), so that P(X > Y) is the measure of interest and X and Y are clearly not independent. Modeling income and consumption as non-identically Dagum distributed variables and their dependence by a Frank copula, we show that the proposed method improves the estimation of household financial fragility. Using data from the 2008 wave of the Bank of Italy’s Survey on Household Income and Wealth we point out that neglecting the existing dependence in fact overestimates the actual household fragility.

Statistical Modeling of Temporal Dependence in Financial Data via a Copula Function

In financial analysis it is useful to study the dependence between two or more time series as well as the temporal dependence in a univariate time series. This article is concerned with the statistical modeling of the dependence structure in a univariate financial time series using the concept of copula. We treat the series of financial returns as a first order Markov process. The Archimedean two-parameter BB7 copula is adopted to describe the underlying dependence structure between two consecutive returns, while the log-Dagum distribution is employed to model the margins marked by skewness and kurtosis. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. Furthermore, we apply the model to the daily returns of four stocks and, finally, we illustrate how its fitting to data can be improved when the dependence between consecutive returns is described through a copula function.

Concomitants of m -generalized order statistics from generalized Farlie-Gumbel-Morgenstern distribution family

In this work, we study the concomitants of m -generalized order statistics (m-GOSs) from generalized Farlie-Gumbel-Morgenstern (GFGM) distribution family as a natural extension of the results by Beg and Ahsanullah (2008). We derive probability density functions, moments and recurrence relations between moments of concomitants of m-GOSs from the GFGM distribution family. Analogous results for order statistics and record values are presented as special cases. Moreover, using the features of the GFGM family and the moments of concomitants of order statistics, we propose three estimators of the dependence parameter of the GFGM family with Dagum distributed marginals.

Graphical models for multivariate Markov chains

The aim of this paper is to provide a graphical representation of the dynamic relations among the marginal processes of a first order multivariate Markov chain. We show how to read Granger-noncausal and contemporaneous independence relations off a particular type of mixed graph, when directed and bi-directed edges are missing. Insights are also provided into the Markov properties with respect to a graph that are retained under marginalization of a multivariate chain. Multivariate logistic models for transition probabilities are associated with the mixed graphs encoding the relevant independencies. Finally, an application on real data illustrates the methodology.

Multiple hidden Markov models for categorical time series

We introduce multiple hidden Markov models (MHMMs) where a multivariate categorical time series depends on a latent multivariate Markov chain. MHMMs provide an elegant framework for specifying various independence relationships between multiple discrete time processes. These independencies are interpreted as Markov properties of a mixed graph and a chain graph associated respectively to the latent and observation components of the MHMM. These Markov properties are also translated into zero restrictions on the parameters of marginal models for the transition probabilities and the distributions of observable variables given the latent states.

Monotone Graphical Multivariate Markov Chains

In this paper, we show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger non-causality, contemporaneous independence and monotone dependence coherent with a stochastic ordering. The tested hypotheses associated to a multi edge graph are proven to be equivalent to equality and inequality constraints on interactions of a multivariate logistic model parameterizing the transition probabilities. As the null hypothesis is specified by inequality constraints, the likelihood ratio statistic has chi-bar-square asymptotic distribution whose tail probabilities can be computed by simulation. The introduced hypotheses are tested on real categorical time series.