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Wagenpfeil, Stefan (1995): Hyperparameter Estimation in Exponential Family State Space Models. Collaborative Research Center 386, Discussion Paper 6
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Abstract

Data-driven hyperparameter estimation or automatic choice of the smoothing parameter is of great importance, especially in the applications. This article presents and compares three methods for hyperparameter estimation in the framework of exponential family state space models: First, we motivate and derive a formula for an approximative likelihood, and an alternative, yet mathematical equivalent, expression proves to be a generalized version of a proposal in Durbin and Koopman (1992). Second, the EM-type algorithm suggested in Fahrmeir (1992) is restated here for reasons of comparison and third, the idea of cross-validation proposed by Kohn and Ansley (1989) for linear state space models is extended to the present context, in particular for multicategorical and multidimensional responses. Finally, we compare the three methods for hyperparameter estimation by applying each on three real data sets.