Open Access
Translator Disclaimer
October, 1991 Strong Limit Theorems of Empirical Functionals for Large Exceedances of Partial Sums of I.I.D. Variables
Amir Dembo, Samuel Karlin
Ann. Probab. 19(4): 1737-1755 (October, 1991). DOI: 10.1214/aop/1176990232

Abstract

Let $(X_i,U_i)$ be pairs of i.i.d. bounded real-valued random variables ($X_i$ and $U_i$ are generally mutually dependent). Assume $E\lbrack X_i\rbrack < 0$ and $\Pr\{X_i > 0\} > 0$. For the (rare) partial sum segments where $\sum^l_{i=k}X_i \rightarrow \infty$, strong limit laws are derived for the sums $\sum^l_{i=k}U_i$. In particular a strong law for the length $(l - k + 1)$ and the empirical distribution of $U_i$ in the event of large segmental sums of $\sum X_i$ are obtained. Applications are given in characterizing the composition of high scoring segments in letter sequences and for evaluating statistical hypotheses of sudden change points in engineering systems.

Citation

Download Citation

Amir Dembo. Samuel Karlin. "Strong Limit Theorems of Empirical Functionals for Large Exceedances of Partial Sums of I.I.D. Variables." Ann. Probab. 19 (4) 1737 - 1755, October, 1991. https://doi.org/10.1214/aop/1176990232

Information

Published: October, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0746.60028
MathSciNet: MR1127724
Digital Object Identifier: 10.1214/aop/1176990232

Subjects:
Primary: 60F15
Secondary: 60F10 , 60G50

Keywords: empirical functionals , large segmental sums , strong laws

Rights: Copyright © 1991 Institute of Mathematical Statistics

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.19 • No. 4 • October, 1991
Back to Top