openHSU – Research Showcase

Forecast error is not only caused by the randomness of the data‐generating process but also by the uncertainty due to estimated model parameters. We investigate these different sources of forecast error for a popular type of count process, the Poisson first‐order integer‐valued autoregressive (INAR(1)) process. However, many of our analytical derivations also hold for the more general family of conditional linear AR(1) (CLAR(1)) processes. In addition, results from a simulation study are presented, to verify and complement our asymptotic approximations.

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators.