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Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung.
In this note, we obtain a Chung's integral test for self-normalized sums of i.i.d. random variables. Furthermore, we obtain a convergence rate of Chung law of the iterated logarithm for self-normalized sums.
Abstract. To derive a Baum-Katz type result, a Chover-type law of the iterated logarithm is established for weighted sums of negatively associated (NA) and identically distributed random variables with a distribution in the domain of a stable law in this paper.
As for ρ∗-mixing sequences of random variables, Bryc and Smoleński  established the moments inequality of partial sums. Peligrad  obtained a CLT and established an invariance principles. Peligrad  established the Rosenthal-type maximal inequality. Utev and Peligrad  obtained invariance principles of nonstationary sequences. As for negatively… (More)
Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. These not only generalize the result of Bai and Cheng (2000, Statist Probab Lett 46: 105-112) to rho*-mixing sequences of random… (More)
We call this a Chover-type LIL (laws of the iterated logarithm). This type LIL has been established by Vasudeva and Divanji , Zinchenko  for delayed sums, by Chen and Huang  for geometric weighted sums, and by Chen  for weighted sums. Qi and Cheng  extended the Chover-type law of the iterated logarithm for the partial sums to the case… (More)
Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.