A semi-parametric estimate of extra-Poisson variation for vital rates

We introduce a method for estimating overdispersion in Poisson models for vital rates. We assume smoothness conditions on the counts to obtain pointwise variance estimates that we combine to obtain an estimate of the overdispersion parameter. We create confidence intervals about the observed rates using this estimate and an approximation based on the gamma distribution. The advantage of this method is that the estimates of the superpopulation rates do not depend on the smoothness assumption, yet when this assumption is met we obtain approximately unbiased estimates of the overdispersion parameter. Thus, we may calculate confidence intervals for vital rates under an overdispersed Poisson model without making parametric assumptions on the mean rates.