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Apresentamos uma aplicação da teoria geral dos testes de distância a modelos com erros nas variáveis. Consideramos o modelo de regressão linear simples com intercepto nulo, o modelo de regressão multivariado e um caso especial deste, o modelo decalibração comparativa. Comparamos, utilizando dados simulados, a função poder do teste de distância para hipóteses com restrições nos parâmetros com as funções poder de outros testes gerais, formulados sem incorporar em suas estruturas assuposições de erros nas variáveis e hipóteses restritas simultaneamente. Sabemos que, quando a matriz jacobiana da função que descreve as restrições nas hipóteses tem posto completo, a distribuição nula assintótica da estatística do teste dedistância é uma mistura de distribuições qui-quadrado. Isto não é necessariamente verdadeiro qiando existem pontos singulares na hipótese nula. Sugerimos uma modificação na estatística de teste que assegura a convergência à uma mistura dedistribuições qui-quadrado. Dois conjuntos de dados reais são analisados de acordo com as técnicas propostasWe present an application of the theory of distance tests to errors-in-variables models. We consider the simple linear regression model with null intercept, the multivariate regression model and a special case of that, the comparative calibrationmodel. We compare, using artificial data, the power function of the distance test for restricted hypotheses with power functions of another general tests that were developed without the assumptions of errors in variables and restrictedhypotheses occurring simultaneously. It is known that, when the jacobian matrix of the restriction function describing the hypotheses has full rank, the asymptotic null distribution of the distance test statistic is a mixture of chi-squaredistributions. This assertion is not necessarily true when there exist singular points in the null hypothesis. We suggest a modification to the test statistic which ensures convergence to a mixture of chi-square distributions. Two sets of realdata are analysed according to the proposed method

mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions

We present the R package mixsmsn, which implements routines for maximum likeli- hood estimation (via an expectation maximization EM-type algorithm) in finite mixture models with components belonging to the class of scale mixtures of the skew-normal distribution, which we call the FMSMSN models. Both univariate and multivariate re- sponses are considered. It is possible to fix the number of components of the mixture to be fitted, but there exists an option that transfers this responsibility to an automated procedure, through the analysis of several models choice criteria. Plotting routines to generate histograms, plug-in densities and contour plots using the fitted models output are also available. The precision of the EM estimates can be evaluated through their esti- mated standard deviations, which can be obtained by the provision of an approximation of the associated information matrix for each particular model in the FMSMSN family. A function to generate artificial samples from several elements of the family is also supplied. Finally, two real data sets are analyzed in order to show the usefulness of the package

Multivariate mixture modeling using skew-normal independent distributions

In this paper we consider a flexible class of models, with elements that are finite mixtures of multivariate skew-normal independent distributions. A general EM-type algorithm is employed for iteratively computing parameter estimates and this is discussed with emphasis on finite mixtures of skew-normal, skew-t, skew-slash and skew-contaminated normal distributions. Further, a general information-based method for approximating the asymptotic covariance matrix of the estimates is also presented. The accuracy of the associated estimates and the efficiency of some information criteria are evaluated via simulation studies. Results obtained from the analysis of artificial and real data sets are reported illustrating the usefulness of the proposed methodology. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn.EM algorithm Multivariate finite mixtures Skew-normal distribution Skew-normal independent distributions

Bayesian density estimation using skew student-t-normal mixtures

We present a Bayesian approach for modeling heterogeneous data and estimate multimodal densities using mixtures of Skew Student-t-Normal distributions [Gómez, H.W., Venegas, O., Bolfarine, H., 2007. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18, 395-407]. A stochastic representation that is useful for implementing a MCMC-type algorithm and results about existence of posterior moments are obtained. Marginal likelihood approximations are obtained, in order to compare mixture models with different number of component densities. Data sets concerning the Gross Domestic Product per capita (Human Development Report) and body mass index (National Health and Nutrition Examination Survey), previously studied in the related literature, are analyzed.

Finite mixture of skewed distributions

This book presents recent results in finite mixtures of skewed distributions to prepare readers to undertake mixture models using scale mixtures of skew normal distributions (SMSN). For this purpose, the authors consider maximum likelihood estimation for univariate and multivariate finite mixtures where components are members of the flexible class of SMSN distributions. This subclass includes the entire family of normal independent distributions, also known as scale mixtures of normal distributions (SMN), as well as the skew-normal and skewed versions of some other classical symmetric distributions: the skew-t (ST), the skew-slash (SSL) and the skew-contaminated normal (SCN), for example. These distributions have heavier tails than the typical normal one, and thus they seem to be a reasonable choice for robust inference. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn, highlighting the applicability of the techniques presented in the book. This work is a useful reference guide for researchers analyzing heterogeneous data, as well as a textbook for a graduate-level course in mixture models. The tools presented in the book make complex techniques accessible to applied researchers without the advanced mathematical background and will have broad applications in fields like medicine, biology, engineering, economic, geology and chemistry

Robust mixture modeling based on scale mixtures of skew-normal distributions

A flexible class of probability distributions, convenient for modeling data with skewness behavior, discrepant observations and population heterogeneity is presented. The elements of this family are convex linear combinations of densities that are scale mixtures of skew-normal distributions. An EM-type algorithm for maximum likelihood estimation is developed and the observed information matrix is obtained. These procedures are discussed with emphasis on finite mixtures of skew-normal, skew-t, skew-slash and skew contaminated normal distributions. In order to examine the performance of the proposed methods, some simulation studies are presented to show the advantage of this flexible class in clustering heterogeneous data and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. A real data set is analyzed, illustrating the usefulness of the proposed methodology.

Needlescopic versus laparoscopic cholecystectomy: a prospective study of 60 patients Colecistectomia agulhascópica versus colecistectomia laparoscópica: um estudo prospectivo de 60 pacientes

PURPOSE: To test the hypothesis that needlescopic cholecystectomies (NC) offer superior outcomes in comparison to common laparoscopic cholecystectomies (LC). METHODS: Sixty consecutive patients with gallbladder disease undergoing either LC or NC were evaluated with respect to differences in operative time, frequency of per-operative incidents, post-operative pain, late postoperative symptoms, length of scars and level of postoperative satisfaction. RESULTS: Mean operative time was similar in both groups. Most of the patients, irrespective of the technique, informed mild postoperative pain. NC patients had lower levels of pain on the 7th postoperative day (PO7) (p<0.01) and decreased need for additional analgesia. Less frequency of epigastric wound pain was observed in NC patients until PO4 (p<0.01). Aesthetic result was far superior after NC (total length of scars less than half after LC). No differences regarding postoperative satisfaction with the operation were observed between the studied groups. CONCLUSIONS: Both techniques were safe and effective, presenting similar operative times and low levels of postoperative pain. Downsizing the ports to 2-3 mm was associated with significantly less frequency of postoperative pain only in the epigastric wound until PO4. Aesthetic outcome of NC was significantly superior to LC, although this advantage did not influence patient level of satisfaction.<br>OBJETIVO: Testar a hipótese de que colecistectomias agulhascópicas oferecem resultados superiores aos da colecistectomia laparoscópica usual (CL). MÉTODOS: Sessenta pacientes consecutivos com colecistopatia submetidos à CA ou CV foram avaliados quanto ao tempo operatório, freqüência de acidentes peroperatórios, dor pós-operatória, sintomas pós-operatórios tardios, comprimento das cicatrizes e grau de satisfação. RESULTADOS: O tempo operatório médio foi semelhante em ambos os grupos. A maioria dos pacientes, independentemente da técnica, relataram dor pós-operatória leve. Aqueles operados por CA tiveram menores níveis de dor no 7º dia de pós-operatório (PO7) (p<0.01) e menor necessidade de analgesia adicional. Menor freqüência de dor epigástrica foi observada no grupo CA até o PO4 (p<0.01). O resultado estético foi amplamente superior após CA (comprimento total das cicatrizes menor que a metade após CL). Não houve diferença quanto ao grau de satisfação entre os grupos. CONCLUSÕES: As duas técnicas foram seguras e eficazes, apresentando tempos operatórios semelhantes e baixos níveis de dor pós-operatória. A redução dos portais para 2-3 mm associou-se a menor freqüência de dor pós-operatória apenas na incisão epigástrica até o PO4. O resultado estético da agulhascopia foi significantemente superior ao da laparoscopia, apesar desta vantagem não ter influenciado o grau de satisfação dos doentes