Asymptotics for the Moment Convergence of <inline-formula> <graphic file="1029-242X-2010-350517-i1.gif"/></inline-formula>-Statistics in LIL
<p/> <p>Let <inline-formula> <graphic file="1029-242X-2010-350517-i2.gif"/></inline-formula> be a <inline-formula> <graphic file="1029-242X-2010-350517-i3.gif"/></inline-formula>-statistic based on a symmetric kernel <inline-form...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/350517 |
| Summary: | <p/> <p>Let <inline-formula> <graphic file="1029-242X-2010-350517-i2.gif"/></inline-formula> be a <inline-formula> <graphic file="1029-242X-2010-350517-i3.gif"/></inline-formula>-statistic based on a symmetric kernel <inline-formula> <graphic file="1029-242X-2010-350517-i4.gif"/></inline-formula> and i.i.d. samples <inline-formula> <graphic file="1029-242X-2010-350517-i5.gif"/></inline-formula>. In this paper, the exact moment convergence rates in the law of the iterated logarithm and the law of the logarithm of <inline-formula> <graphic file="1029-242X-2010-350517-i6.gif"/></inline-formula> are obtained, which extend previous results concerning partial sums.</p> |
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| ISSN: | 1025-5834 1029-242X |