10,738 research outputs found
Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R
This paper describes the R package mhsmm which implements estimation and prediction methods for hidden Markov and semi-Markov models for multiple observation sequences. Such techniques are of interest when observed data is thought to be dependent on some unobserved (or hidden) state. Hidden Markov models only allow a geometrically distributed sojourn time in a given state, while hidden semi-Markov models extend this by allowing an arbitrary sojourn distribution. We demonstrate the software with simulation examples and an application involving the modelling of the ovarian cycle of dairy cows.
S-estimation of hidden Markov models
A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step
with high breakdown S-estimation of location and scatter, performed by using the
bisquare multivariate S-estimator. Estimates are obtained by solving a system of estimating equations that are characterized by component specific sets of weights, based on
robust Mahalanobis-type distances. Convergence of the resulting algorithm is proved
and its finite sample behavior is investigated by means of a brief simulation study and
n application to a multivariate time series of daily returns for seven stock markets
Hierarchical hidden Markov structure for dynamic correlations: the hierarchical RSDC model.
This paper presents a new multivariate GARCH model with time-varying conditional correlation structure which is a generalization of the Regime Switching Dynamic Correlation (RSDC) of Pelletier (2006). This model, which we name Hierarchical RSDC, is building with the hierarchical generalization of the hidden Markov model introduced by Fine et al. (1998). This can be viewed graphically as a tree-structure with different types of states. The first are called production states and they can emit observations, as in the classical Markov-Switching approach. The second are called abstract states. They can't emit observations but establish vertical and horizontal probabilities that define the dynamic of the hidden hierarchical structure. The main gain of this approach compared to the classical Markov-Switching model is to increase the granularity of the regimes. Our model is also compared to the new Double Smooth Transition Conditional Correlation GARCH model (DSTCC), a STAR approach for dynamic correlations proposed by Silvennoinen and Teräsvirta (2007). The reason is that under certain assumptions, the DSTCC and our model represent two classical competing approaches to modeling regime switching. We also perform Monte-Carlo simulations and we apply the model to two empirical applications studying the conditional correlations of selected stock returns. Results show that the Hierarchical RSDC provides a good measure of the correlations and also has an interesting explanatory power.Multivariate GARCH; Dynamic correlations; Regime switching; Markov chain; Hidden Markov models; Hierarchical Hidden Markov models
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Efficient semiparametric estimation and model selection for multidimensional mixtures
In this paper, we consider nonparametric multidimensional finite mixture
models and we are interested in the semiparametric estimation of the population
weights. Here, the i.i.d. observations are assumed to have at least three
components which are independent given the population. We approximate the
semiparametric model by projecting the conditional distributions on step
functions associated to some partition. Our first main result is that if we
refine the partition slowly enough, the associated sequence of maximum
likelihood estimators of the weights is asymptotically efficient, and the
posterior distribution of the weights, when using a Bayesian procedure,
satisfies a semiparametric Bernstein von Mises theorem. We then propose a
cross-validation like procedure to select the partition in a finite horizon.
Our second main result is that the proposed procedure satisfies an oracle
inequality. Numerical experiments on simulated data illustrate our theoretical
results
Algebraic statistical models
Many statistical models are algebraic in that they are defined in terms of
polynomial constraints, or in terms of polynomial or rational parametrizations.
The parameter spaces of such models are typically semi-algebraic subsets of the
parameter space of a reference model with nice properties, such as for example
a regular exponential family. This observation leads to the definition of an
`algebraic exponential family'. This new definition provides a unified
framework for the study of statistical models with algebraic structure. In this
paper we review the ingredients to this definition and illustrate in examples
how computational algebraic geometry can be used to solve problems arising in
statistical inference in algebraic models
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