24 research outputs found
Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields
We prove moment inequalities for a class of functionals of i.i.d. random
fields. We then derive rates in the central limit theorem for weighted sums of
such randoms fields via an approximation by -dependent random fields
Homogeneous kernel integral operators in Grand Lebesgue Spaces
In this short report we estimate and calculate the exact value of norms of
multilinear integral operators having homogeneous kernel, acting between two
Grand Lebesgue Spaces
Local linear spatial quantile regression
Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.Let {(Yi,Xi), i ∈ ZN} be a stationary real-valued (d + 1)-dimensional spatial processes. Denote by x →
qp(x), p ∈ (0, 1), x ∈ Rd , the spatial quantile regression function of order p, characterized by P{Yi ≤
qp(x)|Xi = x} = p. Assume that the process has been observed over an N-dimensional rectangular domain
of the form In := {i = (i1, . . . , iN) ∈ ZN|1 ≤ ik
≤ nk, k = 1, . . . , N}, with n = (n1, . . . , nN) ∈ ZN. We
propose a local linear estimator of qp. That estimator extends to random fields with unspecified and possibly
highly complex spatial dependence structure, the quantile regression methods considered in the context of
independent samples or time series. Under mild regularity assumptions, we obtain a Bahadur representation
for the estimators of qp and its first-order derivatives, from which we establish consistency and asymptotic
normality. The spatial process is assumed to satisfy general mixing conditions, generalizing classical time
series mixing concepts. The size of the rectangular domain In is allowed to tend to infinity at different
rates depending on the direction in ZN (non-isotropic asymptotics). The method provides muchAustralian Research Counci
Norm estimates in Grand Lebesgue Spaces for some operators, including magic square matrices
We extend the classical Lebesgue-Riesz norm estimations for integral
operators acting between different classical Lebesgue-Riesz spaces into the
Grand Lebesgue Spaces, in the general case. As an example we consider matrix
operators acting between finite dimensional Lebesgue-Riesz spaces, especially
generated by means of positive magic squares
Moment and exponential estimation for the distribution of the norms for random matrices martingales
We derive sharp non - asymptotical Lebesgue - Riesz as well as Grand Lebesgue
Space norm estimations for different norms of matrix martingales through these
norms for the correspondent martingale differences and through the entropic
dimension of the extremal points of the unit ball for a basic space. These
estimates allow us to deduce in particular the exponential decreasing tail of
distribution for these norms of matrix martingales. We bring also some examples
in order to show the exactness of the obtained estimations