1,078 research outputs found
Towards deterministic subspace identification for autonomous nonlinear systems
The problem of identifying deterministic autonomous linear and nonlinear systems is studied. A specific version of the theory of deterministic subspace identification for discrete-time autonomous linear systems is developed in continuous time. By combining the subspace approach to linear identification and the differential-geometric approach to nonlinear control systems, a novel identification framework for continuous-time autonomous nonlinear systems is developed
Dimension estimation for autonomous nonlinear systems
The problem of estimating the dimension of the state-space of an autonomous nonlinear system is considered. Assuming that sampled measurements of the output and finitely many of its time derivatives are available, an exhaustive search algorithm able to retrieve the dimension of the minimal state-space realization is proposed. The performance of the algorithm are evaluated on specific nonlinear systems
Extreme Dependence Models
Extreme values of real phenomena are events that occur with low frequency,
but can have a large impact on real life. These are, in many practical
problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991).
To study these events is of fundamental importance. For this purpose,
probabilistic models and statistical methods are in high demand. There are
several approaches to modelling multivariate extremes as described in Falk et
al. (2011), linked to some extent. We describe an approach for deriving
multivariate extreme value models and we illustrate the main features of some
flexible extremal dependence models. We compare them by showing their utility
with a real data application, in particular analyzing the extremal dependence
among several pollutants recorded in the city of Leeds, UK.Comment: To appear in Extreme Value Modelling and Risk Analysis: Methods and
Applications. Eds. D. Dey and J. Yan. Chapman & Hall/CRC Pres
On Multivariate Records from Random Vectors with Independent Components
Let be independent copies of a
random vector with values in and with a
continuous distribution function. The random vector is a
complete record, if each of its components is a record. As we require
to have independent components, crucial results for univariate
records clearly carry over. But there are substantial differences as well:
While there are infinitely many records in case , there occur only
finitely many in the series if . Consequently, there is a terminal
complete record with probability one. We compute the distribution of the random
total number of complete records and investigate the distribution of the
terminal record. For complete records, the sequence of waiting times forms a
Markov chain, but differently from the univariate case, now the state infinity
is an absorbing element of the state space
Some Results on Joint Record Events
Let be independent and identically distributed random
variables on the real line with a joint continuous distribution function .
The stochastic behavior of the sequence of subsequent records is well known.
Alternatively to that, we investigate the stochastic behavior of arbitrary
, under the condition that they are records, without knowing their
orders in the sequence of records. The results are completely different. In
particular it turns out that the distribution of , being a record, is not
affected by the additional knowledge that is a record as well. On the
contrary, the distribution of , being a record, is affected by the
additional knowledge that is a record as well. If has a density, then
the gain of this additional information, measured by the corresponding
Kullback-Leibler distance, is , independent of . We derive the limiting
joint distribution of two records, which is not a bivariate extreme value
distribution. We extend this result to the case of three records. In a special
case we also derive the limiting joint distribution of increments among
records
Statistical Modeling of Spatial Extremes
The areal modeling of the extremes of a natural process such as rainfall or
temperature is important in environmental statistics; for example,
understanding extreme areal rainfall is crucial in flood protection. This
article reviews recent progress in the statistical modeling of spatial
extremes, starting with sketches of the necessary elements of extreme value
statistics and geostatistics. The main types of statistical models thus far
proposed, based on latent variables, on copulas and on spatial max-stable
processes, are described and then are compared by application to a data set on
rainfall in Switzerland. Whereas latent variable modeling allows a better fit
to marginal distributions, it fits the joint distributions of extremes poorly,
so appropriately-chosen copula or max-stable models seem essential for
successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Models for extremal dependence derived from skew-symmetric families
Skew-symmetric families of distributions such as the skew-normal and skew-
represent supersets of the normal and distributions, and they exhibit
richer classes of extremal behaviour. By defining a non-stationary skew-normal
process, which allows the easy handling of positive definite, non-stationary
covariance functions, we derive a new family of max-stable processes - the
extremal-skew- process. This process is a superset of non-stationary
processes that include the stationary extremal- processes. We provide the
spectral representation and the resulting angular densities of the
extremal-skew- process, and illustrate its practical implementation
(Includes Supporting Information).Comment: To appear in Scandinavian Journal of Statistic
Likelihood-based inference for max-stable processes
The last decade has seen max-stable processes emerge as a common tool for the
statistical modeling of spatial extremes. However, their application is
complicated due to the unavailability of the multivariate density function, and
so likelihood-based methods remain far from providing a complete and flexible
framework for inference. In this article we develop inferentially practical,
likelihood-based methods for fitting max-stable processes derived from a
composite-likelihood approach. The procedure is sufficiently reliable and
versatile to permit the simultaneous modeling of marginal and dependence
parameters in the spatial context at a moderate computational cost. The utility
of this methodology is examined via simulation, and illustrated by the analysis
of U.S. precipitation extremes
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