Let be independent zero-mean real valued variables and let Then

Continue reading “Hoeffding’s Inequality”

Advertisements

Skip to content
# Category: Inequalities

# Hoeffding’s Inequality

# An inequality of the mean involving truncation

# Rio’s Inequality

# Kolmogorov’s Maximal Inequality

Let be independent zero-mean real valued variables and let Then

Continue reading “Hoeffding’s Inequality”

Advertisements

Let be i.i.d. r.vs with and . Then

Proof:

First we proove the following useful result

If and then

Note you can find the same lemma on Feller Vol.2 (p. 150) as

Continue reading “An inequality of the mean involving truncation”

Let and be two integrable real-valued random variables and let be the quantile function of . Then if is integrable over we have

where is the a-mixing coefficient.

* Proof:* Set and then

since and

note also that

which implies that

- Let be independent random variables with . Set . Then
*Proof:*LetNotice that and