We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of n jointly distributed random variables. We control the expectation of a randomly selected random variable from n jointly distributed random variables, and present bounds that are at least as tight as the classical maximal inequalities, and much tighter when the distribution of selection index is near deterministic. A new family of information theoretic measures was introduced in the process, which may be of independent interest.
- Convex duality
- Generalized Holder's inequality
- Maximal inequality
- Orlicz function
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty