Fetching the paper…

Reading the bibliography…

2017

Generalizations of Maximal Inequalities to Arbitrary Selection Rules

Jiao, Jiantao, Han, Yanjun, Weissman, Tsachy

Original
PDF
Post on X

Understand

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 were introduced in the process, which may be of independent interest.

Generalizations of Maximal Inequalities to Arbitrary Selection Rules · Around

Built on

H. Hudzik and L. Maligranda, “Amemiya norm equals Orlicz norm in general,” Indagationes Mathematicae , vol. 11, no. 4, pp. 573–585, 2000
2000
Earlier work this paper cites.
D. Pollard. (2005) Asymptopia. [Online]. Available: http://www.stat.yale.edu/˜pollard/Courses/607.spring05/handouts/finite-max.pdf
2005
Earlier work this paper cites.

Similar

S. Boucheron, G. Lugosi, and P. Massart, Concentration inequalities: A nonasymptotic theory of independence . Oxford university press, 2013
Original
2013
Cited alongside, same era.
D. Russo and J. Zou, “How much does your data exploration overfit? controlling bias via information usage,” arXiv preprint arXiv:1511.05219 , 2015
Original
2015
Cited alongside, same era.

Then

J. Jiao, Y. Han, and T. Weissman, “Dependence measures bounding the exploration bias for general measurements,” in Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on . IEEE, 2017
2017
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…