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 variables, but also improve them.
rho*-mixing; Marcinkiewicz-Zygmund strong laws; weighted sums
