Moderate Laws of Large Numbers via Weak Laws

Yu-Lin Chou

No hptjm, OSF Preprints from Center for Open Science

Abstract: By a $moderate$ $law$ $of$ $large$ $numbers$ we mean any theorem whose conclusion includes the $L^{p}$-vanishment of the sequence of the sample means of some centered random variables with $1 \leq p < +\infty$ given. Given any $1 \leq p < +\infty$, we prove a moderate law of large numbers for $L^{p}$-bounded random variables that obey a weak law. Thus our moderate laws in particular complement those obtained from the martingale theory, and establish the counterintuitive fact that (for $L^{p}$-bounded random variables) where there is a weak law there is a moderate law.

Date: 2020-12-01
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:hptjm

DOI: 10.31219/osf.io/hptjm

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