Location: Seminar Room 819, Niels Henrik Abels Hus, 8th floor
Speaker: Hans Rudolf Künsch, Professor Emeritus at the Department of Mathematics of the Swiss Federal Institute of Technology of Zurich
Title: Robust estimation of fixed parameters in state space models
Abstract: A state-space model consists of a latent state process (Xt) with Markovian dynamics and a sequence of conditionally independent partial and noisy observations Yt of Xt. Such models are used in many applications, e.g. ecology, finance or engineering. Often the transition density of (Xt) and/or the conditional density of Yt given Xt contain unknown fixed parameters. In this talk I consider robust estimation methods for such parameters, that is methods which are stable under small deviations from the nominal model. For this, the joint likelihood of states and observations is robustified by reducing the contribution of pairs (Xt1;Xt) and (Xt; Yt) with low likelihood. I will discuss the computation of the robustified marginal likelihood, the correction required for Fisher consistency and the robustness properties of the resulting estimator. For the last point I use the influence functional as defined in Martin and Yohai (1986). The method is illustrated with data assessing the abundance of North Sea pollock.
Joint work with William Aeberhard, Eva Cantoni, Chris Field, Joanna Fleming and Ximin Xu.