Robust Inference for State-Space Models with Skewed Measurement Noise

Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-t-distributed measurement noise. The proposed filter and smoother are compared with conventional low-complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.Comment: 5 pages, 7 figures. Accepted for publication in IEEE Signal Processing Letter

Flexible modelling in statistics: past, present and future

In times where more and more data become available and where the data exhibit rather complex structures (significant departure from symmetry, heavy or light tails), flexible modelling has become an essential task for statisticians as well as researchers and practitioners from domains such as economics, finance or environmental sciences. This is reflected by the wealth of existing proposals for flexible distributions; well-known examples are Azzalini's skew-normal, Tukey's $g$-and-$h$, mixture and two-piece distributions, to cite but these. My aim in the present paper is to provide an introduction to this research field, intended to be useful both for novices and professionals of the domain. After a description of the research stream itself, I will narrate the gripping history of flexible modelling, starring emblematic heroes from the past such as Edgeworth and Pearson, then depict three of the most used flexible families of distributions, and finally provide an outlook on future flexible modelling research by posing challenging open questions.Comment: 27 pages, 4 figure

Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions

The classical mixture of linear experts (MoE) model is one of the widespread statistical frameworks for modeling, classification, and clustering of data. Built on the normality assumption of the error terms for mathematical and computational convenience, the classical MoE model has two challenges: 1) it is sensitive to atypical observations and outliers, and 2) it might produce misleading inferential results for censored data. The paper is then aimed to resolve these two challenges, simultaneously, by proposing a novel robust MoE model for model-based clustering and discriminant censored data with the scale-mixture of normal class of distributions for the unobserved error terms. Based on this novel model, we develop an analytical expectation-maximization (EM) type algorithm to obtain the maximum likelihood parameter estimates. Simulation studies are carried out to examine the performance, effectiveness, and robustness of the proposed methodology. Finally, real data is used to illustrate the superiority of the new model.Comment: 21 pages