Camila Borelli Zeller

Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties

The Generalized Inverse Gaussian (GIG) distribution has found many interesting applications; see Jorgensen [24]. This rich family includes some well-known distributions, such as the inverse Gaussian, gamma and exponential, as special cases. These distributions have been used as the mixing density for building some heavy-tailed multivariate distributions including the normal inverse Gaussian, Student-t and Laplace distributions. In this paper, we use the GIG distribution in the context of the scale-mixture of skew-normal distributions, deriving a new family of distributions called Skew-Normal Generalized Hyperbolic distributions. This new flexible family of distributions possesses skewness with heavy-tails, and generalizes the symmetric normal inverse Gaussian and symmetric generalized hyperbolic distributions.

A robust extension of the bivariate Birnbaum-Saunders distribution and associated inference

We propose here a robust extension of the bivariate Birnbaum-Saunders (BS) distribution derived recently by Kundu et al. (2010). This extension is based on scale mixtures of normal (SMN) distributions that are used for modeling symmetric data. This type of bivariate Birnbaum-Saunders distribution based on SMN models is an absolutely continuous distribution whose marginals are of univariate Birnbaum-Saunders type. We then develop the EM-algorithm for the maximum likelihood (ML) estimation of the model parameters, and illustrate the obtained results with a real data and display the robustness feature of the estimation procedure developed here.

Multivariate measurement error models using finite mixtures of skew-Student t distributions

In regression models, the classical assumption of normal distribution of the random observational errors is often violated, masking some important features of the variability present in the data. Some practical actions to solve the problem, like transformation of variables to achieve normality, are often of doubtful utility. In this work we present a proposal to deal with this issue in the context of the simple linear regression model when both the response and the explanatory variable are observed with error. In such models, the experimenter observes a surrogate variable instead of the covariate of interest. We extend the classical normal model by jointly modeling the unobserved covariate and the random errors by a finite mixture of a skewed version of the Student t distribution. This approach allows us to model data with great flexibility, accommodating skewness, heavy tails and multi-modality. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters of the proposed model, and compare the efficiency of our method with some competitors through the analysis of some artificial and real data.

The bivariate Sinh-Elliptical distribution with applications to Birnbaum-Saunders distribution and associated regression and measurement error models

The bivariate Sinh-Elliptical (BSE) distribution is a generalization of the well-known Riecks (1989) Sinh-Normal distribution that is quite useful in Birnbaum-Saunders (BS) regression model. The main aim of this paper is to define the BSE distribution and discuss some of its properties, such as marginal and conditional distributions and moments. In addition, the asymptotic properties of method of moments estimators are studied, extending some existing theoretical results in the literature. These results are obtained by using some known properties of the bivariate elliptical distribution. This development can be viewed as a follow-up to the recent work on bivariate Birnbaum-Saunders distribution by Kundu et al. (2010) towards some applications in the regression setup. The measurement error models are also introduced as part of the application of the results developed here. Finally, numerical examples using both simulated and real data are analyzed, illustrating the usefulness of the proposed methodology.

Influence analyses of skew-normal/independent linear mixed models

A extension of some diagnostic procedures to skew-normal/independent linear mixed models is discussed. This class provides a useful generalization of normal (and skew-normal) linear mixed models since it is assumed that the random effects and the random error terms follow jointly a multivariate skew-normal/independent distribution. Inspired by the EM algorithm, a local influence analysis for linear mixed models, following Zhu and Lees approach is developed. This is because the observed data log-likelihood function associated with the proposed model is somewhat complex and Cooks well-known approach can be very difficult for obtaining measures of local influence. Moreover, the local influence measures obtained under this approach are invariant under reparameterization. Four specific perturbation schemes are also discussed. Finally, a real data set is analyzed in order to illustrate the usefulness of the proposed methodology.

Statistical analysis and modeling of a novel parameter for resource allocation in multicarrier PLC systems

This work outlines a novel parameter that is capable of characterizing the flatness of the normalized signal-to-noise ratio for resource allocation purposes in power line communication (PLC) systems, which are based on multicarrier modulation schemes. This parameter, named normalized signal-to-noise ratio coherence bandwidth, can be used for grouping adjacent subchannels therefore reducing the computational complexity of resource allocation techniques. Additionally, we discuss a comparative analysis between the proposed parameter and the coherence bandwidth for resource allocation purposes, which leads us to conclude that the former is more appropriate than the latter for PLC systems. Moreover, we show a statistical analysis of the proposed parameter and model it with different distributions based on noise measurements and channel estimates of broadband in-home, outdoor, and hybrid PLC-wireless environments. On the basis of data sets obtained from measurement campaigns covering the frequency bands of 1.7 to 30, 1.7 to 50, and 1.7 to 100 MHz, we show that the best distributions for modeling the proposed parameter are inverse Gaussian, Nakagami, gamma, and Gaussian mixture, depending on the type of the channel (in home, outdoor, and hybrid PLC wireless) and the frequency band.

Statistical modeling of the average channel gain and delay spread in in-home PLC channels

This work describes a complete statistical modeling of the average channel gain in dB (ACGdB) and the root mean squared delay spread (RMS-DS) for power line communication (PLC) systems. The PLC channel features are estimated from 148,037 channel frequency responses measured in 7 typical different places in an urban area in Brazil. Two frequency bands are considered: from 1.7 up to 30 MHz and from 1.7 up to 100 MHz. The resulting datasets for ACGdB and RMS-DS were fitted to well known continuous distributions, including symmetric (Logistic and Normal) and asymmetric (Exponential, Gamma, Inverse Gaussian, Loglogistic, Lognormal, Nakagami, Rayleigh, Rician, Skew-normal, t-Student and Weibull) cases. The best distribution fitted to the considered dataset is indicated by the log-likelihood value and three distinct information criteria. The achieved results revealed that the ACGdB is better modeled by the Skew-normal and the Nakagami distributions for the frequency bands from 1.7 up to 30 MHz and 100 MHz, respectively, whereas the RMS-DS is little bit better modeled by the Gamma distribution, then by the Lognormal distribution, in both frequency bands considered.

The sinh-normal/independent nonlinear regression model

The normal/independent family of distributions is an attractive class of symmetric heavy-tailed density functions. They have a nice hierarchical representation to make inferences easily. We propose the Sinh-normal/independent distribution which extends the Sinh-normal (SN) distribution [23]. We discuss some of its properties and propose the Sinh-normal/independent nonlinear regression model based on a similar setup of Lemonte and Cordeiro [18], who applied the Birnbaum–Saunders distribution. We develop an EM-algorithm for maximum likelihood estimation of the model parameters. In order to examine the robustness of this flexible class against outlying observations, we perform a simulation study and analyze a real data set to illustrate the usefulness of the new model.

Influence diagnostics for the structural sharpe model under normal/independent distributions

ABSTRACT A method is proposed in this paper to assess the local influence of minor perturbations for the Sharpe model when the normal distribution is replaced by normal/independent (NI) distributions. The family of NI distributions is an attractive class of symmetric heavy-tailed densities that includes as special cases the normal, t-Student, slash, and the contaminated normal distributions. Since the returns of the market are not observable, the statistical analysis is carried out in the context of an errors-in-variables model. An influence analysis for detecting influential observations (atypical returns) is developed to investigate the sensitivity of the maximum likelihood estimators. Diagnostic measures are obtained based on the conditional expectation of the complete-data log-likelihood function. The results are illustrated by using a set of shares of companies traded in the Chilean stock market.

Finite mixture of regression models for censored data based on scale mixtures of normal distributions

In statistical analysis, particularly in econometrics, the finite mixture of regression models based on the normality assumption is routinely used to analyze censored data. In this work, an extension of this model is proposed by considering scale mixtures of normal distributions (SMN). This approach allows us to model data with great flexibility, accommodating multimodality and heavy tails at the same time. The main virtue of considering the finite mixture of regression models for censored data under the SMN class is that this class of models has a nice hierarchical representation which allows easy implementation of inferences. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters in the proposed model. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset. The proposed algorithm and methods are implemented in the new R package CensMixReg.