Foregasting with adaptive filtering
Forward estimation for ergodic time series
Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
We introduce a fractional Langevin equation with α-stable noise and show that its solution is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of via the measure of its codependence r(θ₁,θ₂,t). We prove that is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin...
Free area estimation in a dynamic germ-grain model with renewal dropping process.
Functional equations in dynamic programming.
Further applications of the T*-test to time-series analysis
Fuzzy clustering of spatial binary data
An iterative fuzzy clustering method is proposed to partition a set of multivariate binary observation vectors located at neighboring geographic sites. The method described here applies in a binary setup a recently proposed algorithm, called Neighborhood EM, which seeks a partition that is both well clustered in the feature space and spatially regular [AmbroiseNEM1996]. This approach is derived from the EM algorithm applied to mixture models [Dempster1977], viewed as an alternate optimization method...
Gaussian approximation to the partial sum processes of moving averages.
Gaussian limits for random geometric measures.
Gaussian model selection
Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...
Gaussian semiparametric estimation in seasonal/cyclical long memory time series
Gaussian semiparametric or local Whittle estimation of the memory parameter in standard long memory processes was proposed by Robinson [18]. This technique shows several advantages over the popular log- periodogram regression introduced by Geweke and Porter–Hudak [7]. In particular under milder assumptions than those needed in the log periodogram regression it is asymptotically more efficient. We analyse the asymptotic behaviour of the Gaussian semiparametric estimate of the memory parameter in...
General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis
We study ensembles of similar systems under load of environmental factors. The phenomenon of adaptation has similar properties for systems of different nature. Typically, when the load increases above some threshold, then the adapting systems become more different (variance increases), but the correlation increases too. If the stress continues to increase then the second threshold appears: the correlation achieves maximal value, and start to decrease, but the variance continue to increase. In many...
Generalised filtering.
Generalized Levinson-Durbin sequences and binomial coefficients.
Generalized method of least squares collocation
Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.
Genetic linkage analysis: An irregular statistical problem.
Goodness-of-fit tests in long-range dependent processes under fixed alternatives
In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239–258] proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives.
Hazard rate model and statistical analysis of a compound point process
A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process behaviour....
Hellinger integrals, contiguity and entire separation
Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones