A supplement to precise asymptotics in the law of the iterated logarithm for self-normalized sums
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Let X,X1,X2, . . . be i.i.d. random variables with zero means, variance one, and set [수식] Gut and Spataru [3] established the precise asymptotics in the law of the iterated logarithm and Li, Nguyen and Rosalsky [7] generalized their result under minimal conditions. If [수식] is replaced by [수식] in their results, the new one is called the moment version of precise asymptotics in the law of the iterated logarithm. We establish such a result for self-normalized sums, when X belongs to the domain of attraction of the normal law.
Abstract
Let X,X1,X2, . . . be i.i.d. random variables with zero means, variance one, and set [수식] Gut and Spataru [3] established the precise asymptotics in the law of the iterated logarithm and Li, Nguyen and Rosalsky [7] generalized their result under minimal conditions. If [수식] is replaced by [수식] in their results, the new one is called the moment version of precise asymptotics in the law of the iterated logarithm. We establish such a result for self-normalized sums, when X belongs to the domain of attraction of the normal law.
참고문헌 (10)
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