• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.341-348
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• 1994

Some extensions of the law of the iterated logarithm via self-normalization are obtained for seuences of sign-invariant random variables.

• Journal of the Korean Data and Information Science Society
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• 제2권
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• pp.41-44
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• 1991

Petrov (1968) gave two theorems on the law of the iterated logarithm without any assumptions about the existence of moments of independent random variables. In the present paper we show that the same holds true for sign-invariant random variables.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.53-63
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• 1993

We consider various types of weak convergence for sums of sign-invariant random variables. Some results show a similarity between independence and sign-invariance. As a special case, we obtain a result which strengthens a weak law proved by Rosalsky and Teicher [6] in that some assumptions are deleted.

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.293-301
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• 1995

Sums of independent random variables $S_n = X_1 + \cdots + X_n$ are considered, where the $X_n$ are chosen according to a stationary process of distributions. For $c > 0$, let $t_c$ be the smallest positive integer n such that $$\mid$S_n$\mid$ > cn^{\frac{1}{2}}$. In this set up we are concerned with finiteness of expectation of $t_c$ and we have some results of sign-invariant process as applications.