ABSTRACT. The bootstrap method is generally performed by presupposing that each sample unit would show the same probability of being re-sampled. However, when a sample with outliers is taken into account, the empirical distribution generated by this method may be influenced, or rather, it may not accurately represent the original sample. Current study proposes a bootstrap algorithm that allows the use of measures of influence in the calculation of re-sampling probabilities. The method was reproduced in simulation scenarios taking into account the logistic growth curve model and the CovRatio measurement to evaluate the impact of an influential observation in the determinacy of the matrix of the co-variance of parameter estimates. In most cases, bias estimates were reduced. Consequently, the method is suitable to be used in non-linear models and allows the researcher to apply other measures for better bias reductions.Keywords: CovRatio, accuracy, precision, Monte Carlo.Proposta de um procedimento bootstrap utilizando medidas de influência em modelos de regressão não lineares na presença de outliers RESUMO. Em geral o método bootstrap é realizado supondo que cada unidade amostral apresente a mesma probabilidade de ser reamostrada. Contudo, ao considerar uma amostra que apresente outliers, a distribuição empírica gerada através da execução desse método pode ser influenciada, no sentido de não representar fielmente a amostra original. Tendo por base este problema, o objetivo desse trabalho consistiu em propor um algoritmo bootstrap que permita utilizar medidas de influência no cálculo das probabilidades de reamostragem. Com este propósito, a ilustração desse método foi feita em alguns cenários de simulação, considerando o modelo não linear de crescimento logístico e a medida CovRatio, utilizada para avaliar o impacto de uma observação influente no determinante da matriz de covariância das estimativas dos parâmetros. Observou-se que na maioria dos casos as estimativas dos vieses foram reduzidas. Concluiu-se que o método é adequado de ser utilizado em modelos não lineares, permitindo ao pesquisador aplicar outras medidas de tal forma a proporcionar melhor redução do viés.Palavras-chave: CovRatio, acurácia, precisão, Monte Carlo. IntrodutionWhen inferential methods in data analysis have to be applied, the researcher constantly faces atypical observations that are generally interpreted as outliers. The consequence of such observations consists in a breach of assumptions and/or the construction of statistical tests. It may be said that when outliers occur in a sample, the researcher must be very careful in the interpretation of results, since the latter may have been impaired.An alternative consists in the application of robust inferential methods in the occurrence of such issues. While taking into consideration samples from binomial populations within this context, Silva and Cirillo (2010) carried out a study related to the performance of an estimator for the binomial proportion by different concentration of outliers i...
The bootstrap method is generally performed by presupposing that each sample unit would show the same probability of being re-sampled. However, when a sample with outliers is taken into account, the empirical distribution generated by this method may be influenced, or rather, it may not accurately represent the original sample. Current study proposes a bootstrap algorithm that allows the use of measures of influence in the calculation of re-sampling probabilities. The method was reproduced in simulation scenarios taking into account the logistic growth curve model and the CovRatio measurement to evaluate the impact of an influential observation in the determinacy of the matrix of the co-variance of parameter estimates. In most cases, bias estimates were reduced. Consequently, the method is suitable to be used in non-linear models and allows the researcher to apply other measures for better bias reductions.
The multivariate t models are symmetric and have heavier tail than the normal distribution and produce robust inference procedures for applications. In this paper, the Bayesian estimation of a dynamic factor model is presented, where the factors follow a multivariate autoregressive model, using the multivariate t distribution. Since the multivariate t distribution is complex, it was represented in this work as a mix of the multivariate normal distribution and a square root of a chi-square distribution. This method allowed the complete dene of all the posterior distributions. The inference on the parameters was made taking a sample of the posterior distribution through a Gibbs Sampler. The convergence was veried through graphical analysis and the convergence diagnostics of Geweke (1992) and Raftery and Lewis (1992).
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