Deli Li

SOME RESULTS ON TWO-SIDED LIL BEHAVIOR

ni=1 Xi, n � 1. We establish necessary and sufficient conditions for having with probability 1, 0 1 and to h(n) = (log n) r , r > 0, we obtain analogues of the Hartman–Wintner LIL in the infinite variance case. Our proof is based on a general result dealing with LIL behavior of the normalized sums {Sn/cn; n � 1}, where cn is a sufficiently regular normalizing sequence.

CHARACTERIZATION OF LIL BEHAVIOR IN BANACH SPACE

In a recent paper by the authors a general result characterizing two-sided LIL behavior for real valued random variables has been established. In this paper, we look at the corresponding problem in the Banach space setting. We show that there are analogous results in this more general setting. In particularly, we provide a necessary and sufficient condition for LIL behavior with respect to sequences of the form p nh(n), where h is from a suitable subclass of the positive, nondecreasing slowly varying functions. To prove these results we have to use a different method. One of our main tools is an improved Fuk-Nagaev type inequality in Banach space which should be of independent interest.

Some strong limit theorems for the largest entries of sample correlation matrices

Let

Strong convergence in nonparametric regression with truncated dependent data

\{X_{k,i};i\geq 1,k\geq 1\}

The Law of the Logarithm for Weighted Sums of Independent Random Variables

be an array of i.i.d. random variables and let

Complete convergence of bootstrapped means and moments of the supremum of normed bootstrapped sums

\{p_n;n\geq 1\}

Almost sure lim sup behavior of bootstrapped means with applications to pairwise i.i.d. sequences and stationary ergodic sequences

be a sequence of positive integers such that

A large deviation principle for bootstrapped sample means

n/p_n

New Versions of Some Classical Stochastic Inequalities

is bounded away from 0 and

A Supplement to the Einmahl–Li Results on Two-Sided Iterated Logarithm Type Behavior for I.I.D. Random Variables

\infty