44,819 research outputs found
Modeling extreme values of processes observed at irregular time steps: Application to significant wave height
This work is motivated by the analysis of the extremal behavior of buoy and
satellite data describing wave conditions in the North Atlantic Ocean. The
available data sets consist of time series of significant wave height (Hs) with
irregular time sampling. In such a situation, the usual statistical methods for
analyzing extreme values cannot be used directly. The method proposed in this
paper is an extension of the peaks over threshold (POT) method, where the
distribution of a process above a high threshold is approximated by a
max-stable process whose parameters are estimated by maximizing a composite
likelihood function. The efficiency of the proposed method is assessed on an
extensive set of simulated data. It is shown, in particular, that the method is
able to describe the extremal behavior of several common time series models
with regular or irregular time sampling. The method is then used to analyze Hs
data in the North Atlantic Ocean. The results indicate that it is possible to
derive realistic estimates of the extremal properties of Hs from satellite
data, despite its complex space--time sampling.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS711 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Semiparametric estimation of spectral density function for irregular spatial data
Estimation of the covariance structure of spatial processes is of fundamental
importance in spatial statistics. In the literature, several non-parametric and
semi-parametric methods have been developed to estimate the covariance
structure based on the spectral representation of covariance functions.
However,they either ignore the high frequency properties of the spectral
density, which are essential to determine the performance of interpolation
procedures such as Kriging, or lack of theoretical justification. We propose a
new semi-parametric method to estimate spectral densities of isotropic spatial
processes with irregular observations. The spectral density function at low
frequencies is estimated using smoothing spline, while a parametric model is
used for the spectral density at high frequencies, and the parameters are
estimated by a method-of-moment approach based on empirical variograms at small
lags. We derive the asymptotic bounds for bias and variance of the proposed
estimator. The simulation study shows that our method outperforms the existing
non-parametric estimator by several performance criteria.Comment: 29 pages, 2 figure
Power-law statistics and universal scaling in the absence of criticality
Critical states are sometimes identified experimentally through power-law
statistics or universal scaling functions. We show here that such features
naturally emerge from networks in self-sustained irregular regimes away from
criticality. In these regimes, statistical physics theory of large interacting
systems predict a regime where the nodes have independent and identically
distributed dynamics. We thus investigated the statistics of a system in which
units are replaced by independent stochastic surrogates, and found the same
power-law statistics, indicating that these are not sufficient to establish
criticality. We rather suggest that these are universal features of large-scale
networks when considered macroscopically. These results put caution on the
interpretation of scaling laws found in nature.Comment: in press in Phys. Rev.
ON DISCRETE SAMPLING OF TIME-VARYINGCONTINUOUS-TIME SYSTEMS
We consider a multivariate continuous time process, generated by a system of linear stochastic differential equations, driven by white noise and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing significantly simplifies matters). Such settings represent partial extensions of ones studied extensively by A.R. Bergstrom. A model for the observed time series is deduced. Initially we focus on a first-order model, but higher-order ones are discussed in case of equally-spaced observations. Some discussion of issues of statistical inference is included.Stochastic differential equations, time-varying coefficients, discrete sampling, irregular sampling.
Some Computational Aspects of Gaussian CARMA Modelling
Representation of continuous-time ARMA, CARMA, models is reviewed. Computational aspects of simulating and calculating the likelihood-function of CARMA are summarized. Some numerical properties are illustrated by simulations. Some real data applications are shown.CARMA, maximum-likelihood, spectrum, Kalman filter, computation
- …