ProbabilityTheoryMeasureTheoryLargeDeviationsStatistics
We would like concentration inequalities for wider classes of random variables than Bernoulli or Normal. In particular we would like to consider the most general random variables that obey Hoeffding’s Inequality: considering just one random variables we get that we desire a constant such that the tails of lie below a Gaussian tail: . Since any random variable’s distribution is uniquely defined by it’s Moment Generating Function, a random variable is called a ()-subgaussian random variable if there exists such that
Maximal Inequality
Given -subgaussian r.v.’s (not necessarily independent) then