On the Maximal Inequalities for Partial Sums of Strong Mixing Random Variables with Applications: Guo-dong Xing, Shan-chao Yang - Team, Support (Thai Journal of Mathematics, 2011)
Maximal inequalities for partial sums of strong mixing random variables are established. To show the applications of the inequalities obtained, we discuss the strong consistency of Gasser-M¨uller estimator of fixed design regression estimate and obtain the almost sure convergence rate n^-1/2log log n)^1/ξlog^3/2n with any 0<ξ<2, which closes to the optimal achievable convergence rate for independent random variables under an iterated logarithm.