Robust estimation methods for a class of log-linear count time series models

We study robust estimation of a log-linear Poisson model for count time series analysis. More specifically, we study robust versions of maximum likelihood estimators (MLEs) under three different forms of interventions: additive outliers (AOs), transient shifts (TSs) and level shifts (LSs). We estimate the parameters using the MLE, the conditionally unbiased bounded-influence estimator and the Mallows quasi-likelihood estimator and compare all three estimators in terms of their mean-square error, bias and mean absolute error. Our empirical results illustrate that under a LS or a TS there are no significant differences among the three estimators and the most interesting results are obtained in the presence of AOs. The results are complemented by a real data example

Mallows’ quasi-likelihood estimation for log-linear Poisson autoregressions

We consider the problems of robust estimation and testing for a log-linear model with feedback for the analysis of count time series. We study inference for contaminated data with transient shifts, level shifts and additive outliers. It turns out that the case of additive outliers deserves special attention. We propose a robust method for estimating the regression coefficients in the presence of interventions. The resulting robust estimators are asymptotically normally distributed under some regularity conditions. A robust score type test statistic is also examined. The methodology is applied to real and simulated data

On Outliers and Interventions in Count Time Series following GLMs

We discuss the analysis of count time series following generalised linear models in the presence of outliers and intervention effects. Different modifications of such models are formulated which allow to incorporate, detect and to a certain degree distinguish extraordinary events (interventions) of different types in count time series retrospectively. An outlook on extensions to the problem of robust parameter estimation, identification of the model orders by robust estimation of autocorrelations and partial autocorrelations, and online surveillance by sequential testing for outlyingness is provided.

The impact of change in the 2007 English law on mental health act detentions

BackgroundThe Mental Health Act (MHA) 2007 made some significant changes from the Mental Health Act 1983, including the fact that detention is now only allowed if an appropriate medical treatment is available to the patient at the time [1]. There was considerable concern at the time that the 2007 Act would lead to an increase in detentions.ObjectiveThe primary objective is to assess how the change in the English law with the MHA 2007 has affected the number of detentions under the MHA.MethodsA retrospective, observational and noninterventional study used anonymised and routinely collected data regarding 11,509 people who were formally assessed under the Mental Health Act during the period of 2001–2011 in the county of Norfolk. This included 7885 assessments before the 2007 MHA and 3620 done after implementation.ResultsThe proportion of people detained following assessment decreased from 53.2% before the 2007 MHA to 42.9% after implementation (P = .000). The total proportion of patients admitted (whether informally or detained) also decreased from 63.3% before the 2007 MHA to 52.8% thereafter (P = .000).ConclusionThese results show a significant decrease in the rate of detentions under the MHA since the 2007 Act became law.Disclosure of interestThe authors have not supplied their declaration of competing interest.</jats:sec