Development of Saddlepoint Methodologies for Sparse Sample Multiple Parameter Generalized Linear Models and Correlated Data Scenarios

Parameter estimation using maximum likelihood techniques may be biased when sample sizes are small, event rates are low, or otherwise sparse counts exist in a parametric model. This in turn may lead researchers to draw invalid statistical conclusions when conventional methods are utilized. The saddlepoint approximation has potential to lessen the degree of bias in sparse data conditions through its use of moments beyond the mean and variance, which allows for more accurate approximations using a smaller number of observations. We propose two novel saddlepoint methods for use in practical analysis scenarios, as an alternative to maximum likelihood estimation. First, we develop a multivariate saddlepoint approximation for use in generalized linear models that allows for estimation and hypothesis testing of multiple model parameters simultaneously using the saddlepoint approach. Second, we develop a saddlepoint approximation method for use in clustered data scenarios. We demonstrate these methods to be suitable alternatives in small sample and sparse data conditions.