TY - JOUR

T1 - Asymptotics of some empirical functionals under long range dependence

AU - Mukherjee, Kanchan

AU - Majumdar, Suman

PY - 1997

Y1 - 1997

N2 - This paper obtains the asymptotic representation of the supremum of a class of functionals of the empirical distribution, with application to estimating the strength of a bundle of parallel filaments, when the observations are strongly dependent. Unlike the case of weakly dependent observations discussed by P. K. Sen and B. B. Bhattacharyya [Z. Wahrsch. Verw. Gebiete 34 (1976), no. 2, 113–118], the limiting distributions of these functionals are not always normal. The nature of the limiting distribution depends heavily on the Hermite rank of a class of indicator functions, and the rate of convergence is much slower in this case (compared to the case of weak dependence). A law of iterated logarithm (LIL) for these functionals is also derived.

AB - This paper obtains the asymptotic representation of the supremum of a class of functionals of the empirical distribution, with application to estimating the strength of a bundle of parallel filaments, when the observations are strongly dependent. Unlike the case of weakly dependent observations discussed by P. K. Sen and B. B. Bhattacharyya [Z. Wahrsch. Verw. Gebiete 34 (1976), no. 2, 113–118], the limiting distributions of these functionals are not always normal. The nature of the limiting distribution depends heavily on the Hermite rank of a class of indicator functions, and the rate of convergence is much slower in this case (compared to the case of weak dependence). A law of iterated logarithm (LIL) for these functionals is also derived.

KW - Long range dependence

KW - Hermite rank

M3 - Journal article

VL - 59

SP - 88

EP - 101

JO - Sankhya - Series A

JF - Sankhya - Series A

SN - 0581-572X

ER -