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We discuss robust M-estimation of INARCH models for count time series. These models assume the observation at each point in time to follow a Poisson distribution conditionally on the past, with the conditional mean being a linear function of previous observations. This simple linear structure allows us to transfer M-estimators for autoregressive models to this situation, with some simplifications being possible because the conditional variance given the past equals the conditional mean. We investigate the performance of the resulting generalized M-estimators using simulations. The usefulness of the proposed methods is illustrated by real data examples. [ABSTRACT FROM AUTHOR]

There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a “weighted scores method”, which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our method is robust and nearly as efficient as maximum likelihood for fully specified copula models. An illustrative example is given to show the use of our weighted scores method to analyze utilization of health care based on family characteristics. [ABSTRACT FROM PUBLISHER]

Abstract: The excess of zeros is not a rare feature in count data. Statisticians advocate the Poisson-type hurdle model (among other techniques) as an interesting approach to handle this data peculiarity. However, the frequency of gross errors and the complexity intrinsic to some considered phenomena may render this classical model unreliable and too limiting. In this paper, we develop a robust version of the Poisson hurdle model by extending the robust procedure for GLM of to the truncated Poisson regression model. The performance of the new robust approach is then investigated via a simulation study, a real data application and a sensitivity analysis. The results show the reliability of the new technique in the neighborhood of the truncated Poisson model. This robust modelling approach is therefore a valuable complement to the classical one, providing a tool for reliable statistical conclusions and to take more effective decisions. [ABSTRACT FROM AUTHOR]