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A Proposal for Robust Estimation of Fixed Parameters in General State-Space Models Aeberhard, William


State-space models (SSMs) encompass a wide range of popular models encountered in various fields such as mathematical finance, control engineering and ecology. SSMs are essentially characterized by a hierarchical structure, with latent variables governed by Markovian dynamics. Fixed parameters in these models are traditionally estimated by maximum likelihood and generally include regression and auto- regression coefficients as well as correlations and scale parameters. Standard robust estimation techniques from generalized linear and time series models cannot be directly adapted to SSMs, and this mainly for two reasons: first, integrating high-dimensional latent variables out of a joint likelihood inevitably requires some approximation (except in very special cases); second, the approximated maximum likelihood scores are typically exceedingly complicated, if not intractable. We propose a robust estimating method based on an unpublished 2001 paper by Shinto Eguchi and Yutaka Kano: instead of introducing weights at the estimating equations level, we downweight observations on the log-likelihood scale. A Laplace approximation of the marginal log-likelihood allows us to formulate a computable estimator for which we derive the influence functional for different scenarios of additive outliers. We resort to indirect inference for the computation of Fisher consistency correction terms.

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