Let Fn(x) be the empirical distribution function based on n independent random variables X1,...,Xn from a common distribution function F(x), and let be the sample mean. We derive the rate of convergence of to normality (for the regular as well as nonregular cases), a law of iterated logarithm,...

A new approach to the asymptotic normality of the multivariate linear rank statistics is provided along with the Berry-Esséen and the Prohorov distance estimates for the remainder term in the convergence to normality.

Nonparametric factorial designs for multivariate observations are considered under the framework of general rank-score statistics. Unlike most of the literature, we do not assume the continuity of the underlying distribution functions. The models studied include general repeated measures...

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.

Suppose {Xn}n[greater-or-equal, slanted]1 are stochastic processes all of whose paths are nonnegative and lie in the space of right continuous functions with finite left limits. Moreover, assume that Xn (properly normalized) converges weakly to a process X, i.e., for some deterministic function...

We study prediction for vector valued random fields in a nonparametric setting. The prediction problem is formulated as the problem if estimating certain conditional expectations and a speed of uniform a.s. convergence is obtained, modifying results for conditional empirical processes derived...

In this paper we show that almost every sample function of the N-parameter Bessel process associated with the N-parameter Wiener process has a local maximum. In addition some properties related to the local maxima are investigated.

Yoshihara (1976) established the weak invariance theorem of the generalized U-statistic for absolutely regular variables but only for the stationary case. In this paper we extend the results from the stationary case to the nonstationary case.

K. I. Yoshihara (1990,Comput. Math. Appl.19, No. 1, 149-158) proved the weak invariance of the conditional nearest neighbor regression function estimator called the conditional empirical process based on[phi]-mixing observations. In this paper, we extend the result for nonstationary and...