2025/05/23 by Hill, Jonathan B.
#60-F25 #60F10 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2505.17800
We derive an Lq-maximal inequality for zero mean dependent random variables \xt\t=1n on ℝp, where p >> % n is allowed. The upper bound is a familiar multiple of ln (p) and an % l∞ moment, as well as Kolmogorov distances based on Gaussian approximations (ρn,ρn), derived with and without negligible truncation and sub-sample blocking. The latter arise due to a departure from independence and therefore a departure from standard symmetrization arguments. Examples are provided demonstrating (ρn,% ρn) → 0 under heterogeneous mixing and physical dependence conditions, where (ρn,ρn) are multiples of ln (p)/nb for some b > 0 that depends on memory, tail decay, the truncation level and block size.