arXiv subjects

Antonio Punzo

Publications and source records attributed to Antonio Punzo.

40 records · Page 3Linked to original sources

arXiv2012

Generalized Linear Gaussian Cluster-Weighted Modeling

Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling the joint probability of data coming from a heterogeneous population as a weighted sum of the products of marginal distributions and conditional distributions. In this paper, we introduce a wide family of Cluster Weighted models in which the conditional distributions are assumed to belong to the exponential family with canonical links which will be referred to as Generalized Linear Gaussian Cluster Weighted Models. Moreover, we show that, in a suitable sense, mixtures of generalized linear models can be considered as nested in Generalized Linear Gaussian Cluster Weighted Models. The proposal is illustrated through many numerical studies based on both simulated and real data sets.

stat.ME↗

arXiv2012

DBKGrad: An R Package for Mortality Rates Graduation by Fixed and Adaptive Discrete Beta Kernel Techniques

Kernel smoothing represents a useful approach in the graduation of mortality rates. Though there exist several options for performing kernel smoothing in statistical software packages, there have been very few contributions to date that have focused on applications of these techniques in the graduation context. Also, although it has been shown that the use of a variable or adaptive smoothing parameter, based on the further information provided by the exposed to the risk of death, provides additional benefits, specific computational tools for this approach are essentially absent. Furthermore, little attention has been given to providing methods in available software for any kind of subsequent analysis with respect to the graduated mortality rates. To facilitate analyses in the field, the R package DBKGrad is introduced. Among the available kernel approaches, it considers a recent discrete beta kernel estimator, in both its fixed and adaptive variants. In this approach, boundary bias is automatically reduced and age is pragmatically considered as a discrete variable. The bandwidth, fixed or adaptive, is allowed to be manually given by the user or selected by cross-validation. Pointwise confidence intervals, for each considered age, are also provided. An application to mortality rates from the Sicily Region (Italy) for the year 2008 is also presented to exemplify the use of the package.

stat.CO↗

arXiv2012

Clustering and Classification via Cluster-Weighted Factor Analyzers

In model-based clustering and classification, the cluster-weighted model constitutes a convenient approach when the random vector of interest constitutes a response variable Y and a set p of explanatory variables X. However, its applicability may be limited when p is high. To overcome this problem, this paper assumes a latent factor structure for X in each mixture component. This leads to the cluster-weighted factor analyzers (CWFA) model. By imposing constraints on the variance of Y and the covariance matrix of X, a novel family of sixteen CWFA models is introduced for model-based clustering and classification. The alternating expectation-conditional maximization algorithm, for maximum likelihood estimation of the parameters of all the models in the family, is described; to initialize the algorithm, a 5-step hierarchical procedure is proposed, which uses the nested structures of the models within the family and thus guarantees the natural ranking among the sixteen likelihoods. Artificial and real data show that these models have very good clustering and classification performance and that the algorithm is able to recover the parameters very well.

stat.ME↗

arXiv2012

Flexible Mixture Modeling with the Polynomial Gaussian Cluster-Weighted Model

In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the mixture components by considering a polynomial regression. Secondly, it is not restricted to be used for model-based clustering only being contextualized in the most general model-based classification framework. Maximum likelihood parameter estimates are derived using the EM algorithm and model selection is carried out using the Bayesian information criterion (BIC) and the integrated completed likelihood (ICL). The paper also investigates the conditions under which the posterior probabilities of component-membership from a polynomial Gaussian CWM coincide with those of other well-established mixture-models which are related to it. With respect to these models, the polynomial Gaussian CWM has shown to give excellent clustering and classification results when applied to the artificial and real data considered in the paper.

stat.ME↗