Let {Xn} be a strictly stationary [phi]-mixing process with [Sigma]j=1[infinity] [phi]1/2(j) [infinity]. It is shown in the paper that if X1 is uniformly distributed on the unit interval, then, for any t [set membership, variant] [0, 1], Fn-1(t) - t + Fn(t) - t = O(n-3/4(log log n)3/4) a.s. and...

Certain results on large deviation probabilities for linear and m-dependent processes are considered here.

It is shown in this note that the one-term Edgeworth expansion for the standardized sample mean of n independent lattice random vectors when perturbed by a random variable (1/[radical sign]n) U is the same as in the strongly non-lattice case, where U is a bounded random variable depending only...

The r-quick limit points of normalized sample paths and empirical distribution functions of mixing processes are characterized. An r-quick version of Bahadur-Kiefer-type representation for sample quantiles is established, which yields the r-quick limit points of quantile processes. These results...

The validity of the one-term Edgeworth expansion is proved for the multivariate mean of a random sample drawn without replacement under a limiting non-latticeness condition on the population. The theorem is applied to deduce the one-term expansion for the univariate statistics which can be...

An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the...