Marcinkiewicz strong laws for linear statistics of rho*-mixing sequences of random variables

Abstract

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 ρ * -mixing sequences of random variables, but also improve them.

Strong and Weak Convergence for Asymptotically Almost Negatively Associated Random Variables

“…A common expression for these linear statistics is = ∑ =1 . Some recent results on the strong law for linear statistics can be found in Cuzick [1], Bai et al [2], Bai and Cheng [3], Cai [4], Wu [5], Sung [6], Zhou et al [7], and Wang et al [8]. Our emphasis in this paper is focused on the result of Bai and Cheng [3].…”