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.