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In this paper we propose an new approach to multivariate collective models based on asymptotic distibutions, since the modeling problems posed have large samples. Collective risk models play an important part in Risk Theory and in Actuarial Mathematics. Inference based on these models is centered on claims totals. However, the new approach has in mind a different kind of risk, the risk of forest fires, where the variables of interest are the number fires and the total burnt areas. As a result, a special case bivariate risk model is derived with this intent. Besides single models, structured families whose models correspond to the treatments of a base linear model are considered. This leads to an ANOVA-like situation where we don't have to estimate the error, which enable to test the influence of several factors on the multivariate collective models mean vectors. Instead of F tests, we use χ 2 tests, availing us of asymptotic distributions that lightens the treatment. To illustrate the approach, an application to forest fires in Portugal with real data is presented. [ABSTRACT FROM AUTHOR]

The high level of unemployment is a major problem in most European countries nowadays. Hence, the demand for small area labor market statistics has rapidly increased over the past few years. The Portuguese Labour Force Survey is the main source of official statistics at the macro level. However, it was not designed to produce reliable design-based statistics at the micro level due to small sample sizes. The goal of this article is to analyze the performance of model-based small area estimators to esthnate the unemployment rate at micro level. Our results showed that the temporal estimator is the most suitable. [ABSTRACT FROM AUTHOR]