Desenvolvimento de novas alternativas de estimadores shrinkage para dados de contagens com sub e superdispersão

Abstract

In this study, alternatives of shrinkage estimators applied to count data models were explored. For this purpose, the work is structured in two parts: the first corresponds to the theoretical back- ground, and the second comprises two articles. In the first article, modified shrinkage estimators were proposed to assess multicollinearity in samples with overdispersion, with a modification of ridge estimators suggested in order to obtain more accurate estimates in Poisson and Negative Binomial models. The results showed that the proposed estimator exhibited greater efficiency and robustness for small samples with high correlation, while maintaining competitiveness in other scenarios. The second article presents a methodological framework consisting of the ex- tension of ridge regression models to the Generalized Poisson model, as well as the adaptation of a set of shrinkage parameters described in the literature. This model is characterized by its flexibility in incorporating a parameter that accounts for the degree of underdispersion and overdispersion. The adapted estimators showed better performance compared to maximum like- lihood estimators in the estimation of regression coefficients, contributing to increased accuracy of standard error estimates and mean squared error. To validate the proposal, Monte Carlo simu- lations were conducted under different scenarios. In addition, two illustrative applications are presented: the first considering a scenario of overdispersion and the second of underdispersion, showing that the adapted ridge estimators demonstrated consistent performance with respect to the evaluated estimates. Finally, the empirical results were found to be in agreement with the simulation findings.