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- GUANG-HUI CAI
- 2006

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.

- Guang-Hui Cai
- Anais da Academia Brasileira de Ciências
- 2008

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.

- Guang-hui Cai
- 2007

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 [1] established the moments inequality of partial sums. Peligrad [10] obtained a CLT and established an invariance principles. Peligrad [11] established the Rosenthal-type maximal inequality. Utev and Peligrad [16] obtained invariance principles of nonstationary sequences. As for negatively… (More)

- Guang-Hui Cai
- Anais da Academia Brasileira de Ciências
- 2006

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)

- GUANG-HUI CAI
- 2006

We call this a Chover-type LIL (laws of the iterated logarithm). This type LIL has been established by Vasudeva and Divanji [13], Zinchenko [14] for delayed sums, by Chen and Huang [3] for geometric weighted sums, and by Chen [2] for weighted sums. Qi and Cheng [11] extended the Chover-type law of the iterated logarithm for the partial sums to the case… (More)

- Guang-Hui Cai
- 2007

- GUANG-HUI CAI, HANG WU, Guang-hui Cai, Hang Wu
- 2005

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.

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