The estimation of the location parameter of a spherically symmetric distribution was greatly improved by Berger and Brandwein. But the authors conditions on the shrinkage estimators depend upon the complete knowledge, up to the location parameter, of the distribution of the observations. We give...

Necessary and sufficient conditions are established for the bounded and compact laws of the iterated logarithm for empirical processes indexed by classes of functions which have the Vapnik-Cervonenkis property. Results of Ledoux and Talagrand (Ann. Probab. 16 1242-1264, and in press) reduce the...

A construction method is developed which enables us to establish the well-known approximation results of Komlós, Major, Tusnády (Z. Wahrsch. Verw. Gebiete34 33-58) in the multidimensional setting. The basic tool is a large deviation theorem for conditional distribution functions which may be...

In this paper we define a robust conditional location functional without requiring any moment condition. We apply the nonparametric proposals considered by C. Stone (Ann. Statist. 5 (1977), 595-645) to this functional equation in order to obtain strongly consistent, robust nonparametric...

We study sufficient conditions under which a sequence of stochastic processes (Xn(t))t >= 0 can be approximated almost surely by another sequence of stochastic processes (Yn(t))t >= 0. Two different approaches are discussed.

Let B be a 2-parameter Brownian motion on R+2. Consider the non-Markovian stochastic differential equation in the plane dX(z) = [alpha](z, X) dB(z) + [beta](z, X)dz for z [set membership, variant] R+2, i.e., Xs, t - X0, t - Xs, 0 + X0, 0 = [integral operator]Rz [alpha]([zeta], X) dB[zeta] +...

We generalize the theorems of Helson-Szegö and Helson-Sarason for matricial measures. We study two-weighted inequalities for the Hilbert transform in [0, 2[pi]] and in R and give a characterization for the positivity of the angle between past and future of multivariate weakly stationary...

Using relatively recent results from multivariate distribution theory, the expectation of a ratio of quadratic forms in normal variables is obtained. Infinite series expressions involving the invariant polynomials of matrix argument are derived. Convergence of the solution depends upon the...

Harel and Puri (1989, J. Multivariate Anal. 29) studied the asymptotic behavior of the U-statistic and the one-sample rank order statistic for nonstationary absolutely regular processes. In this note, we present some applications of these results for Markov processes as well as ARMA processes.

Consider the linear regression model y(n) = x1(n)[theta]1 + ... + xk(n)[theta]k + w(n) with w(n) assumed a linear time series, especially an ARMA series. Procedures which use recursions only are suggested to identify the non-zero [theta]k and the order of ARMA or subset ARMA residuals. The...