1,977 research outputs found
A strong invariance principle for associated random fields
In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] strong
invariance principle for associated sequences to the multi-parameter case,
under the assumption that the covariance coefficient u(n) decays exponentially
as n\to \infty. The main tools that we use are the following: the Berkes and
Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multi-parameter blocking
technique, the Csorgo and Revesz [Z. Wahrsch. Verw. Gebiete 31 (1975) 255-260]
quantile transform method and the Bulinski [Theory Probab. Appl. 40 (1995)
136-144] rate of convergence in the CLT.Comment: Published at http://dx.doi.org/10.1214/009117904000001071 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Linear SPDEs with harmonizable noise
Using tools from the theory of random fields with stationary increments, we
introduce a new class of processes which can be used as a model for the noise
perturbing an SPDE. This type of noise (called harmonizable) is not necessarily
Gaussian, but it includes the spatially homogeneous Gaussian noise introduced
in Dalang (1999), and the fractional noise considered in Balan and Tudor
(2010). We derive some general conditions for the existence of a random field
solution of a linear SPDE with harmonizable noise, under some mild conditions
imposed on the Green function of the differential operator which appears in
this equation. This methodology is applied to the study of the heat and wave
equations (possibly replacing the Laplacian by one of its fractional powers),
extending in this manner the results of Balan and Tudor (2010) to the case
.Comment: 31 page
Asymptotic results with generalized estimating equations for longitudinal data
We consider the marginal models of Liang and Zeger [Biometrika 73 (1986)
13-22] for the analysis of longitudinal data and we develop a theory of
statistical inference for such models. We prove the existence, weak consistency
and asymptotic normality of a sequence of estimators defined as roots of
pseudo-likelihood equations.Comment: Published at http://dx.doi.org/10.1214/009053604000001255 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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