A second-order stochastic process X is called almost periodically correlated (PC) in the sense of Gladyshev if its mean function m(t) and covariance R(t + [tau], t) are uniformly continuous with respect to t, [tau] and are almosst periodic functions of t for every [tau]. We show that the mean...

The only Kagan-n,2(loc) probability measure with Gaussian conditional structure of the second order (GCS2) is a multivariate normal distribution. Also a short review of the known results on the GCS2 distributions is given.

The so-called "other law of the iterated logarithm" was first given by Chung (Trans. Amer. Math. Soc.64 (1948), 205-233) and Mogul'skii (Theor. Probab. Appl.24 (1979), 405-413) respectively for a sequence of independent random variables and for the standard empirical process. In this work, we...

In this paper, we study the weak invariance of the multidimensional rank statistic when the underlying random variables are nonstationary absolutely regular.

We derive the asymptotic distributions for measures of multivariate skewness and kurtosis defined by Malkovich and Afifi if the underlying distribution is elliptically symmetric. A key step in the derivation is an approximation by suitable Gaussian processes defined on the surface of the unit...

In this paper we propose nonparametric estimates of the regression function and its derivative when it is only assumed a weak error's structure. We study their local and global asymptotic behaviour when we observe dependent trajectories.

We consider singular diffusions on k. Under a verifiable criterion for the stability in distribution of such diffusions, a broad subset of the range of the infinitesimal generator of the diffusion is identified. For functions in this set functional central limit theorems and laws of iterated...

Let (X, Y) be a random vector such that X is d-dimensional, Y is real valued, and [theta](X) is the conditional [alpha]th quantile of Y given X, where [alpha] is a fixed number such that 0 < [alpha] < 1. Assume that [theta] is a smooth function with order of smoothness p > 0, and set r = (p - m)/(2p + d), where m is a nonnegative integer smaller than p. Let T([theta]) denote a...</[alpha]>

A version of an asymptotic estimation problem of the unknown variance in a multivariate location-scale parameter family is studied under a general loss function. The asymptotic inadmissibility of the traditional estimator is established. In a particular case we derive an admissible improvement...

Bounds for higher-order cumulants of statistics arising from a linear time series regression model are investigated. A result given in Brillinger is proved and extended. The bounds permit derivation of asymptotic moments and asymptotic normality for estimators of parameters in the model. Two...