Summary We consider estimation for a multivariate location family. Between all confidence regions with volume less than a fixed value L , we find the equivariant confidence region with the biggest coverage probability. This region maximizes the infimum of the coverage probability over all...

We consider the following linear regression model:

We discuss the asymptotic linearization of multivariate M-estimators, when the limit distribution is stable. We consider two different types of kernels: VC and bracketing. When applied to the case of normal limits, our work improves the known results to obtain the limit distribution of...

We present two new tests for normality based on U-processes. These tests improve on the Lilliefors tests. We obtain the consistency and asymptotic null distribution of these tests. We present simulations of the power of these tests and of several classical tests for some fixed alternatives....

It is known that the uniform weak convergence of a sequence of stochastic processes is equivalent to the finite dimensional convergence, plus an asymptotic equicontinuity condition with respect to any pseudometric which makes the parameter space totally bounded. Here, we see that in this...

A Bernstein-type inequality for non-degenerated U-statistics is presented. As the Bernstein inequality for sums of independent identically distributed random variables, in the limit, its tail has the same order as the tail of the limit. We also consider the case of U-processes indexed by a...

The strong law of the large numbers for U-statistics has been proved for a sequence of independent random variables using martingale techniques. We see that the condition of independence can be relaxed to 2m-wise independence. In this case martingale techniques cannot be applied. We also...

We discuss the weak convergence of convex stochastic processes. Let {Zn(t):t [set membership, variant] T}, n [greater-or-equal, slanted] 1, be a sequence of stochastic processes, where T is an open convex set of , such that is a convex function (for each [omega] and each n). We show that...

We prove the asymptotic normality of the trimmed mean, obtained by deleting the data which is further away from a parameter of location [theta]n. To get this trimmed mean, equivariant by rotations, dilations and translations, we choose [theta]n in a class of multivariate parameters of location,...