Moment free deviation inequalities for linear combinations of independent random variables with power-type tails

2022/07/05 by Fresen, Daniel J.
#46N30 #60E05 #60E15 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2207.01867

Abstract

We present order of magnitude estimates for the quantiles of non-negative linear combinations of non-negative random variables, as well as deviation inequalities for general linear combinations of independent random variables, under the assumption that all random variables satisfy the same power-type tail bound on ℙ\\vert X_i\vert>t\ of the form t^-q, t^-q/2 or t^-q/2(ln t)^q/2, for q>2. The third type is applicable in the nonlinear setting. In the situations we consider, these results improve on classical estimates of Nagaev.

Related

• Lower bounds for tails of sums of independent symmetric random variables
• A note on sums of independent random variables
• Tail estimates for random variables from interrelation between corresponding moments inequalities
• Moment and tail estimation for U-statistics with positive kernels
• Tight Chernoff-Like Bounds Under Limited Independence