Traditionally, claim counts and amounts are assumed to be independent in non-life insurance. This paper explores how this oft unwarranted assumption can be relaxed in a simple way while incorporating rating factors into the model. The approach consists of fitting generalized linear models to the marginal frequency and the conditional severity components of the total claim cost; dependence between them is induced by treating the number of claims as a covariate in the model for the average claim size. In addition to being easy to implement, this modeling strategy has the advantage that when Poisson counts are assumed together with a log-link for the conditional severity model, the resulting pure premium is the product of a marginal mean frequency, a modified marginal mean severity, and an easily interpreted correction term that reflects the dependence. The approach is illustrated through simulations and applied to a Canadian automobile insurance dataset.

The following details the proof of the balancing property of the dynamic weights shown in Theorem 2.1 and Remark 2.2 of the paper.

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In this paper, we consider some potential pitfalls of the growing use of quasi-likelihood-based information criteria for longitudinal data to select a working correlation structure in a generalized estimating equation framework. In particular, we examine settings where the fully conditional mean does not equal the marginal mean as well as hypothesis testing following selection of the working correlation matrix. Our results suggest that the use of any information criterion for selection of the working correlation matrix is inappropriate when the conditional mean model assumption is violated. We also find that type I error differs from the nominal level in moderate sample sizes following selection of the form of the working correlation but improves as sample size is increased as the selection is then concentrated on a single correlation structure. Our results serve to underline the potential dangers that can arise when using information criteria to select correlation structure in routine data analysis.

Introduction Research on the health of older Veterans in Canada is an emerging area. Few population-based studies in Canada have included older Veterans as a specific group of interest. This paper describes a cohort of self-identified Veterans within the Canadian Longitudinal Study on Aging (CLSA). Materials and Methods Using data from the CLSA baseline assessment (2011-2015), we describe sociodemographic and health characteristics along with military-related variables in a cohort of Veterans in Canada. We also estimate the number of Canadian and non-Canadian Veterans living in Canada at the time of the CLSA baseline data collection. Results We estimate that at the CLSA baseline, there were 718,893 (95% confidence interval [CI], 680,033-757,110) Canadian Veterans and 185,548 (95% CI, 165,713-205,100) non-Canadian Veterans aged 45-85 years living in Canada. Veterans were older and predominantly male compared to non-Veterans in the CLSA. Following age and sex adjustment, the distribution of sociodemographic and health characteristics was similar across all groups. The majority (> 85%) of participants in each comparison group reported self-rated general and mental health as excellent, very good, or good. Following age and sex adjustment, most characteristics across groups remained similar. One exception was mental health, where a greater proportion of Veterans screened positive for depression and anxiety relative to non-Veterans. Conclusions Using CLSA baseline data, we estimate the number of older Veterans in Canada and present descriptive data that highlight interesting differences and similarities between Veterans and non-Veterans living in Canada. Canadian and non-Canadian Veterans in the CLSA are presented separately, with the latter group having not been previously studied in Canada. This paper presents a snapshot of a cohort of self-identified Veterans within the CLSA at study baseline and highlights the potential of the CLSA as a vehicle for studying the aging Veteran population in Canada for years to come.