Sub-exponential Random Variables

Junwei Lu
Additional contact information
Junwei Lu: Harvard University

Chapter Chapter 5 in Big Data Analysis, 2025, pp 23-28 from Springer

Abstract: Abstract In the previous chapter, we showed the concentration of sample average in the Hoeffding inequality. The asymptotic results like law of large numbers and central limit theorem are also about the sample average. If we look into the proof of these results, we can find that these results rely on the additive formality of the sample mean. So we have the impression that the concentration principle works for the average, but does it cover other statistics? In fact, we have many nonlinear estimators in statistics and machine learning. Can we expect that a general statistic f ( X 1 , … , X n ) $$f(X_1, \ldots, X_n)$$ concentrates to its expectation? The answer is positive. Sample mean is not special.

Date: 2025
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-03161-7_5

Ordering information: This item can be ordered from
http://www.springer.com/9783032031617

DOI: 10.1007/978-3-032-03161-7_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().