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.
Publié le : 1991-10-14
Classification:
Strong laws,
large segmental sums,
empirical functionals,
60F15,
60F10,
60G50
@article{1176990232,
author = {Dembo, Amir and Karlin, Samuel},
title = {Strong Limit Theorems of Empirical Functionals for Large Exceedances of Partial Sums of I.I.D. Variables},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 1737-1755},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990232}
}
Dembo, Amir; Karlin, Samuel. Strong Limit Theorems of Empirical Functionals for Large Exceedances of Partial Sums of I.I.D. Variables. Ann. Probab., Tome 19 (1991) no. 4, pp. 1737-1755. http://gdmltest.u-ga.fr/item/1176990232/