An unobserved components model in which the signal is buried in noise that is nonGaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers.We describe an observation driven model, based on a conditional Student t-distribution, that is tractable and retains some of the desirable features of the linear Gaussian model. Letting the dynamics be driven by the score of the conditional distribution leads to a specification that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The methods are illustrated with an application to rail travel in the UK. The final part of the article shows how the model may be extended to include explanatory variables.

We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum counterpart of classical Fisher information, which has been found to constitute an upper bound for classical information itself [Braunstein and Caves (1994) Phys. Rev. Lett. 72 3439-3443]. It has then become of relevant interest among statisticians, who investigated the relations between classical and quantum information and derived a condition for equality in the particular case of two-dimensional pure state systems [Barndorff-Nielsen and Gill (2000) J. Phys. A 33 4481-4490]. In this paper we show that this condition holds even in the more general setting of two-dimensional mixed state systems. We also derive the expression of the maximum Fisher information achievable and its relation with that attainable in pure states.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000043

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The paper focuses on the adaptation of local polynomial filters at the end of the sample period. We show that for real time estimation of signals (i.e., exactly at the boundary of the time support) we cannot rely on the automatic adaptation of the local polynomial smoothers, since the direct real time filter turns out to be strongly localized, and thereby yields extremely volatile estimates. As an alternative, we evaluate a general family of asymmetric filters that minimizes the mean square revision error subject to polynomial reproduction constraints; in the case of the Henderson filter it nests the well-known Musgrave's surrogate filters. The class of filters depends on unknown features of the series such as the slope and the curvature of the underlying signal, which can be estimated from the data. Several empirical examples illustrate the effectiveness of our proposal

This note is concerned with the spectral properties of matrices associated with linear smoothers. We derive analytical results on the eigenvalues and eigenvectors of smoothing matrices by interpreting the latter as perturbations of matrices belonging to algebras with known spectral properties, such as the circulant and the generalized tau. These results are used to characterize the properties of a smoother in terms of an approximate eigen-decomposition of the associated smoothing matrix.